Search: quadratic-zeroes

Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि द्विघात ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटता है तो उसके वास्तविक शून्यक कैसे होंगे?

If a quadratic graph cuts the (x)-axis at two distinct points, what kind of real zeroes does it have?

Explanation opens after your attempt

Correct Answer

A. दो भिन्न वास्तविक शून्यकTwo distinct real zeroes

Step 1

Concept

Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes. Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.

Step 3

Exam Tip

दो अलग कटान दो अलग वास्तविक शून्यक देते हैं। ग्राफ में अलग (x)-प्रतिच्छेद अलग शून्यक होते हैं।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

किस स्थिति में द्विघात बहुपद के दो वास्तविक शून्यक होंगे?

In which case will a quadratic polynomial have two real zeroes?

Explanation opens after your attempt

Correct Answer

A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटेWhen its graph cuts the (x)-axis at two distinct points

Step 1

Concept

Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.

Step 2

Why this answer is correct

The correct answer is A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points. Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.

Step 3

Exam Tip

द्विघात बहुपद के वास्तविक शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। दो अलग कटाव दो वास्तविक शून्यक देते हैं।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को ((2,0)) और ((7,0)) पर काटता है, तो शून्यक कौन-से हैं?

If the graph of a quadratic polynomial cuts the (x)-axis at ((2,0)) and ((7,0)), what are the zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (7)(2) and (7)

Step 1

Concept

Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).

Step 2

Why this answer is correct

The correct answer is A. (2) और (7) / (2) and (7). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).

Step 3

Exam Tip

शून्यक (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (2) और (7) हैं।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि परवलय (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है, तो द्विघात बहुपद के कितने शून्यक होंगे?

If a parabola cuts the (x)-axis at two distinct points, how many zeroes does the quadratic polynomial have?

Explanation opens after your attempt

Correct Answer

A. दोTwo

Step 1

Concept

The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो / Two. The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.

Step 3

Exam Tip

द्विघात बहुपद का ग्राफ परवलय होता है। (x)-अक्ष पर दो अलग-अलग कटाव दो वास्तविक शून्यक बताते हैं।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि परवलय के शून्यक (-4) और (10) हैं तथा वह नीचे की ओर खुलता है तो शून्यकों के बाहर ग्राफ कहाँ होगा?

If a parabola has zeroes (-4) and (10) and opens downward, where will the graph be outside the zeroes?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.

Step 3

Exam Tip

नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: खुलने की दिशा संकेत क्षेत्र बदलती है।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि परवलय के शून्यक (-2) और (8) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?

If a parabola has zeroes (-2) and (8) and opens downward, where will the graph be outside the zeroes?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.

Step 3

Exam Tip

नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: खुलने की दिशा संकेत क्षेत्र बदलती है।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी परवलय के शून्यक (-1) और (7) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?

If a parabola has zeroes (-1) and (7) and opens downward, where will the graph be outside the zeroes?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

For a downward-opening parabola, values outside the zeroes are negative. Tip: when the direction changes, sign regions also change.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: when the direction changes, sign regions also change.

Step 3

Exam Tip

नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: दिशा बदलने पर संकेत क्षेत्र भी बदलता है।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद के वास्तविक शून्यक (5), (5), (-1) हैं तो अलग वास्तविक शून्यक कौन से हैं?

If the real zeroes of a polynomial are (5), (5), (-1), what are the distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. (5) और (-1)(5) and (-1)

Step 1

Concept

The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.

Step 2

Why this answer is correct

The correct answer is A. (5) और (-1) / (5) and (-1). The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.

Step 3

Exam Tip

दोहराया (5) अलग शून्यक में एक बार ही गिना जाता है। टिप: अलग मानों की सूची बनाएं।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद के वास्तविक शून्यक (2), (2) और (-5) लिखे हैं, तो अलग वास्तविक शून्यक कौन से हैं?

If the real zeroes of a polynomial are written as (2), (2) and (-5), what are the distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (-5)(2) and (-5)

Step 1

Concept

The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-5) / (2) and (-5). The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.

Step 3

Exam Tip

दोहराया (2) अलग शून्यक में एक बार गिना जाता है। टिप: अलग शून्यक में समान मान पुनः न लिखें।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?

If \(\sqrt{2}\) and \(\sqrt{8}\) are zeroes of a quadratic polynomial, what is the sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. \(3\sqrt{2}\)

Step 1

Concept

Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.

Step 2

Why this answer is correct

The correct answer is A. \(3\sqrt{2}\). Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.

Step 3

Exam Tip

क्योंकि \(\sqrt{8}=2\sqrt{2}\), योग \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। पहले करणी को सरल करें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी द्विघात बहुपद (p(x)) का ग्राफ (x)-अक्ष को (-2) और (5) पर काटता है तो उसके शून्यकों की संख्या क्या है?

If the graph of a quadratic polynomial (p(x)) cuts the (x)-axis at (-2) and (5), how many zeroes does it have?

Explanation opens after your attempt

Correct Answer

A. दोTwo

Step 1

Concept

A zero occurs where the graph meets the (x)-axis. In exams count the (x)-intercepts.

Step 2

Why this answer is correct

The correct answer is A. दो / Two. A zero occurs where the graph meets the (x)-axis. In exams count the (x)-intercepts.

Step 3

Exam Tip

ग्राफ जहाँ (x)-अक्ष को काटता है वही शून्यक होता है। परीक्षा में काटने वाले बिंदुओं की संख्या गिनें।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी द्विघात बहुपद के वास्तविक शून्यक (1) और (4) हैं तो उसका आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?

If a quadratic polynomial has real zeroes (1) and (4) then at which points will its graph cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. ((1,0)) और ((4,0))((1,0)) and ((4,0))

Step 1

Concept

A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.

Step 2

Why this answer is correct

The correct answer is A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0)). A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.

Step 3

Exam Tip

शून्यक (a) से कटान बिंदु ((a,0)) बनता है। टिप: शून्यक को (y)-निर्देशांक न बनाएं।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?

If (p(x)=x^-2-6x+8), which monic polynomial has the squares of its zeroes as zeroes?

Explanation opens after your attempt

Correct Answer

A. \(x^2-20x+64\)

Step 1

Concept

The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-20x+64\). The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).

Step 3

Exam Tip

मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-2dx+d^-2-36) है, तो ग्राफ के शून्यक कौन से होंगे?

If (p(x)=x^-2-2dx+d^-2-36), what will be the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (d-6) और (d+6)(d-6) and (d+6)

Step 1

Concept

It is ((x-d)²-36), so \(x-d=\pm6\) and the zeroes are (d-6), (d+6). Tip: use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (d-6) और (d+6) / (d-6) and (d+6). It is ((x-d)²-36), so \(x-d=\pm6\) and the zeroes are (d-6), (d+6). Tip: use difference of squares.

Step 3

Exam Tip

यह ((x-d)²-36) है, इसलिए \(x-d=\pm6\) और शून्यक (d-6), (d+6) हैं। टिप: वर्गों के अंतर का उपयोग करें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-19x+90) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

If (p(x)=x^-2-19x+90), what is the distance between the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.

Step 3

Exam Tip

(x^-2-19x+90=(x-9)(x-10)) है, इसलिए दूरी (10-9=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-2-2cx+c^-2-25) है, तो ग्राफ के शून्यक कौन से होंगे?

If (p(x)=x^-2-2cx+c^-2-25), what will be the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (c-5) और (c+5)(c-5) and (c+5)

Step 1

Concept

It is ((x-c)²-25), so \(x-c=\pm5\) and the zeroes are (c-5), (c+5). Tip: use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (c-5) और (c+5) / (c-5) and (c+5). It is ((x-c)²-25), so \(x-c=\pm5\) and the zeroes are (c-5), (c+5). Tip: use difference of squares.

Step 3

Exam Tip

यह ((x-c)²-25) है, इसलिए \(x-c=\pm5\) और शून्यक (c-5), (c+5) हैं। टिप: वर्गों के अंतर का उपयोग करें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-2-17x+72) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

If (p(x)=x^-2-17x+72), what is the distance between the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-17x+72=(x-8)(x-9)), so the distance is (9-8=1). Tip: find zeroes first and then take distance.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-17x+72=(x-8)(x-9)), so the distance is (9-8=1). Tip: find zeroes first and then take distance.

Step 3

Exam Tip

(x^-2-17x+72=(x-8)(x-9)) है, इसलिए दूरी (9-8=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-2bx+b^-2-16) है तो ग्राफ के शून्यक कौन से होंगे?

If (p(x)=x^-2-2bx+b^-2-16), what will be the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (b-4) और (b+4)(b-4) and (b+4)

Step 1

Concept

It is ((x-b)²-16), so \(x-b=\pm4\) and the zeroes are (b-4), (b+4). Tip: use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (b-4) और (b+4) / (b-4) and (b+4). It is ((x-b)²-16), so \(x-b=\pm4\) and the zeroes are (b-4), (b+4). Tip: use difference of squares.

Step 3

Exam Tip

यह ((x-b)²-16) है इसलिए \(x-b=\pm4\) और शून्यक (b-4), (b+4) हैं। टिप: वर्गों के अंतर का उपयोग करें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2-15x+56) है तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

If (p(x)=x^-2-15x+56), what is the distance between the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-15x+56=(x-7)(x-8)), so the distance is (8-7=1). Tip: find zeroes first and then take distance.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-15x+56=(x-7)(x-8)), so the distance is (8-7=1). Tip: find zeroes first and then take distance.

Step 3

Exam Tip

(x^-2-15x+56=(x-7)(x-8)) है इसलिए दूरी (8-7=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-2ax+a^-2-9) है, तो ग्राफ के शून्यक कौन से होंगे?

If (p(x)=x^-2-2ax+a^-2-9), what will be the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (a-3) और (a+3)(a-3) and (a+3)

Step 1

Concept

It is ((x-a)²-9), so \(x-a=\pm3\) and the zeroes are (a-3), (a+3). Tip: use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (a-3) और (a+3) / (a-3) and (a+3). It is ((x-a)²-9), so \(x-a=\pm3\) and the zeroes are (a-3), (a+3). Tip: use difference of squares.

Step 3

Exam Tip

यह ((x-a)²-9) है, इसलिए \(x-a=\pm3\) और शून्यक (a-3), (a+3) हैं। टिप: वर्गों के अंतर का उपयोग करें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-2-13x+42) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

If (p(x)=x^-2-13x+42), what is the distance between the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-13x+42=(x-6)(x-7)), so the distance is (7-6=1). Tip: find zeroes first and then take distance.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-13x+42=(x-6)(x-7)), so the distance is (7-6=1). Tip: find zeroes first and then take distance.

Step 3

Exam Tip

(x^-2-13x+42=(x-6)(x-7)) है, इसलिए दूरी (7-6=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-2-11x+30) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

If (p(x)=x^-2-11x+30), what is the distance between the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-11x+30=(x-5)(x-6)), so the distance is (6-5=1). Tip: find zeroes first and then take the distance.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-11x+30=(x-5)(x-6)), so the distance is (6-5=1). Tip: find zeroes first and then take the distance.

Step 3

Exam Tip

(x^-2-11x+30=(x-5)(x-6)), इसलिए दूरी (6-5=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-2+x-6) है तो वास्तविक शून्यक कौन से हैं?

If (p(x)=x^-2+x-6), what are the real zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (-3)(2) and (-3)

Step 1

Concept

(x^-2+x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-3) / (2) and (-3). (x^-2+x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.

Step 3

Exam Tip

(x^-2+x-6=(x+3)(x-2)) इसलिए शून्यक (-3) और (2) हैं। टिप: गुणनखंडों के चिह्न ध्यान से पढ़ें।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=2x^-2-8) है तो ग्राफ के शून्यक कौन से हैं?

If (p(x)=2x^-2-8), what are the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (2) और (-2)(2) and (-2)

Step 1

Concept

From \(2x^2-8=0\), \(x^2=4\) and \(x=\pm2\). Tip: simplify by the common factor first.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-2) / (2) and (-2). From \(2x^2-8=0\), \(x^2=4\) and \(x=\pm2\). Tip: simplify by the common factor first.

Step 3

Exam Tip

\(2x^2-8=0\) से \(x^2=4\) और \(x=\pm2\) मिलता है। टिप: पहले समान गुणक से सरल करें।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=-x^-2+25), तो ग्राफ के वास्तविक शून्यक कौन से होंगे?

If (p(x)=-x^-2+25), what will be the real zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (5) और (-5)(5) and (-5)

Step 1

Concept

From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).

Step 2

Why this answer is correct

The correct answer is A. (5) और (-5) / (5) and (-5). From \(-x^2+25=0\), \(x^2=25\), so \(x=\pm5\). Tip: even with a negative sign, set (y=0).

Step 3

Exam Tip

\(-x^2+25=0\) से \(x^2=25\), इसलिए \(x=\pm5\) है। टिप: ऋण चिह्न देखकर भी (y=0) रखना न भूलें।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी परवलय के दो वास्तविक शून्यक हैं, तो वह (x)-अक्ष से कैसे मिलेगा?

If a parabola has two real zeroes, how will it meet the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. दो अलग-अलग बिंदुओं पर काटेगाIt will cut at two distinct points

Step 1

Concept

Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.

Step 2

Why this answer is correct

The correct answer is A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points. Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.

Step 3

Exam Tip

दो वास्तविक शून्यक दो अलग (x)-अक्ष कटाव बताते हैं। इसलिए परवलय (x)-अक्ष को दो बिंदुओं पर काटेगा।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को नहीं छूता। उसके विविक्त वास्तविक शून्यकों की संख्या क्या होगी?

A quadratic polynomial graph does not touch the (x)-axis. What is the number of distinct real zeroes?

Explanation opens after your attempt

Correct Answer

A. शून्यZero

Step 1

Concept

For a real zero the graph must meet the (x)-axis. No meeting means no real zero.

Step 2

Why this answer is correct

The correct answer is A. शून्य / Zero. For a real zero the graph must meet the (x)-axis. No meeting means no real zero.

Step 3

Exam Tip

वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। कोई मिलन नहीं तो कोई वास्तविक शून्यक नहीं।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी द्विघात बहुपद के ग्राफ का शीर्ष (x)-अक्ष पर है तो वास्तविक शून्यकों के बारे में क्या सही है?

If the vertex of a quadratic polynomial graph lies on the (x)-axis, what is correct about its real zeroes?

Explanation opens after your attempt

Correct Answer

A. दोनों वास्तविक शून्यक समान हैंBoth real zeroes are equal

Step 1

Concept

When the vertex lies on the (x)-axis, the parabola touches the axis at one point. Hence the zeroes are equal.

Step 2

Why this answer is correct

The correct answer is A. दोनों वास्तविक शून्यक समान हैं / Both real zeroes are equal. When the vertex lies on the (x)-axis, the parabola touches the axis at one point. Hence the zeroes are equal.

Step 3

Exam Tip

शीर्ष (x)-अक्ष पर होने पर परवलय अक्ष को एक ही बिंदु पर छूता है। इसलिए शून्यक समान होते हैं।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

एक द्विघात बहुपद का ग्राफ (x)-अक्ष को एक ही बिंदु ((4,0)) पर छूता है। उसके शून्यक कैसे होंगे?

The graph of a quadratic polynomial touches the (x)-axis at only one point ((4,0)). What type of zeroes does it have?

Explanation opens after your attempt

Correct Answer

A. बराबर शून्यक (4) और (4)Equal zeroes (4) and (4)

Step 1

Concept

When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.

Step 2

Why this answer is correct

The correct answer is A. बराबर शून्यक (4) और (4) / Equal zeroes (4) and (4). When a quadratic graph touches at one point its two zeroes are equal. Treat it as a repeated zero in exams.

Step 3

Exam Tip

द्विघात ग्राफ एक बिंदु पर छूता है तो दोनों शून्यक समान होते हैं। परीक्षा में इसे दोहराया शून्यक मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी द्विघात ग्राफ का शीर्ष ((3,-4)) है और वह ऊपर की ओर खुलता है, तो वास्तविक शून्यकों की संख्या क्या होगी?

If a quadratic graph has vertex ((3,-4)) and opens upward, what will be the number of real zeroes?

Explanation opens after your attempt

Correct Answer

C. दोTwo

Step 1

Concept

The vertex is below the (x)-axis and the graph opens upward, so it cuts the (x)-axis twice. Tip: check vertex height and opening direction together.

Step 2

Why this answer is correct

The correct answer is C. दो / Two. The vertex is below the (x)-axis and the graph opens upward, so it cuts the (x)-axis twice. Tip: check vertex height and opening direction together.

Step 3

Exam Tip

शीर्ष (x)-अक्ष के नीचे है और ग्राफ ऊपर खुलता है, इसलिए वह (x)-अक्ष को दो बार काटेगा। टिप: शीर्ष की ऊँचाई और खुलने की दिशा साथ देखें।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

द्विघात बहुपद का ग्राफ नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?

The graph of a quadratic polynomial opens downward and cuts the (x)-axis at two points. What is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

C. दोTwo

Step 1

Concept

The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is C. दो / Two. The opening direction does not change the count, there are two intersections. Tip: decide zeroes by (x)-axis intersections.

Step 3

Exam Tip

दिशा ऊपर या नीचे होने से संख्या नहीं बदलती, कटान दो हैं। टिप: शून्यकों की संख्या (x)-अक्ष कटान से तय करें।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी द्विघात बहुपद का परवलय (x)-अक्ष को केवल ((3,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यकों की संख्या क्या होगी?

If the parabola of a quadratic polynomial only touches the (x)-axis at ((3,0)), what is the number of distinct real zeroes?

Explanation opens after your attempt

Correct Answer

B. एकOne

Step 1

Concept

The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.

Step 2

Why this answer is correct

The correct answer is B. एक / One. The touching point gives only one distinct zero (3). Tip: count a repeated zero once when distinct zeroes are asked.

Step 3

Exam Tip

स्पर्श बिंदु केवल एक अलग शून्यक (3) देता है। टिप: दोहराए हुए शून्यक को अलग शून्यक में एक बार गिनें।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि द्विघात बहुपद का आलेख (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?

If the graph of a quadratic polynomial cuts the (x)-axis at two distinct points then what is the number of real zeroes?

Explanation opens after your attempt

Correct Answer

A. दोTwo

Step 1

Concept

Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.

Step 2

Why this answer is correct

The correct answer is A. दो / Two. Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.

Step 3

Exam Tip

दो कटान बिंदु दो वास्तविक शून्यक बताते हैं। टिप: परवलय (x)-अक्ष को अधिकतम दो बार काट सकता है।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी परवलय का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो द्विघात बहुपद के वास्तविक शून्यक कितने होंगे?

If a parabola has no common point with the (x)-axis, how many real zeroes does the quadratic polynomial have?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.

Step 2

Why this answer is correct

The correct answer is A. (0). Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.

Step 3

Exam Tip

वास्तविक शून्यक तभी मिलते हैं जब ग्राफ (x)-अक्ष से मिले। साझा बिंदु न होने पर वास्तविक शून्यक (0) होंगे।

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Question Easy Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि परवलय पूरा (x)-अक्ष के ऊपर है, तो द्विघात बहुपद के कितने वास्तविक शून्यक होंगे?

If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?

Explanation opens after your attempt

Correct Answer

A. कोई नहींNone

Step 1

Concept

If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.

Step 2

Why this answer is correct

The correct answer is A. कोई नहीं / None. If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.

Step 3

Exam Tip

यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो (p(x)=0) का कोई वास्तविक मान नहीं मिलता। इसलिए वास्तविक शून्यक (0) होंगे।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(3+\sqrt{2}\) और \(3-\sqrt{2}\) किसी बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?

If \(3+\sqrt{2}\) and \(3-\sqrt{2}\) are zeroes of a polynomial, what is the sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The sum is (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6). In exams the sum of conjugate zeroes is always rational.

Step 2

Why this answer is correct

The correct answer is A. (6). The sum is (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6). In exams the sum of conjugate zeroes is always rational.

Step 3

Exam Tip

योग (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6) है। परीक्षा में संयुग्मी शून्यकों का योग हमेशा परिमेय होता है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

किस बहुपद में शून्यकों का योग परिमेय है लेकिन दोनों शून्यक अपरिमेय हैं?

Which polynomial has a rational sum of zeroes but both zeroes are irrational?

Explanation opens after your attempt

Correct Answer

A. \(x^2-4x+1\)

Step 1

Concept

In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+1\). In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.

Step 3

Exam Tip

\(x^2-4x+1\) में योग (4) है और (D=16-4=12) से शून्यक अपरिमेय हैं। परिमेय योग का अर्थ परिमेय शून्यक होना नहीं है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

किस बहुपद के शून्यक वास्तविक हैं लेकिन परिमेय नहीं हैं?

Which polynomial has real zeroes but not rational zeroes?

Explanation opens after your attempt

Correct Answer

C. \(x^2-8\)

Step 1

Concept

From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.

Step 2

Why this answer is correct

The correct answer is C. \(x^2-8\). From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.

Step 3

Exam Tip

\(x^2-8=0\) से \(x=\pm2\sqrt{2}\), जो अपरिमेय वास्तविक हैं। पूर्ण वर्ग और धनात्मकता दोनों जाँचें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी बहुपद का ग्राफ (x)-अक्ष को केवल सम संख्याओं (-4), (2), और (8) पर काटता है। शून्यकों की संख्या क्या है?

A polynomial graph cuts the (x)-axis only at the even numbers (-4), (2), and (8). What is the number of zeroes?

Explanation opens after your attempt

Correct Answer

A. तीनThree

Step 1

Concept

Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.

Step 2

Why this answer is correct

The correct answer is A. तीन / Three. Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.

Step 3

Exam Tip

तीन अलग (x)-प्रतिच्छेद तीन शून्यक देते हैं। संख्या के प्रकार से नहीं बल्कि प्रतिच्छेदों से गिनें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

ग्राफ (x)-अक्ष को काटता नहीं बल्कि (y=2) रेखा को दो बार काटता है। शून्यकों के बारे में क्या निश्चित है?

The graph does not cut the (x)-axis but cuts the line (y=2) twice. What is certain about zeroes?

Explanation opens after your attempt

Correct Answer

A. दिए गए आधार पर कोई शून्यक नहीं दिखताNo zero is shown from the given data

Step 1

Concept

Zeroes are linked only with the (x)-axis where (y=0). Intersections with (y=2) do not show zeroes.

Step 2

Why this answer is correct

The correct answer is A. दिए गए आधार पर कोई शून्यक नहीं दिखता / No zero is shown from the given data. Zeroes are linked only with the (x)-axis where (y=0). Intersections with (y=2) do not show zeroes.

Step 3

Exam Tip

शून्यक केवल (x)-अक्ष यानी (y=0) से जुड़े होते हैं। (y=2) से प्रतिच्छेद शून्यक नहीं बताता।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि परवलय नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?

If a parabola opens downward and cuts the (x)-axis at two points, how many real zeroes will it have?

Explanation opens after your attempt

Correct Answer

A. दोTwo

Step 1

Concept

The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो / Two. The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.

Step 3

Exam Tip

खुलने की दिशा शून्यकों की संख्या अकेले तय नहीं करती। दो कटान स्पष्ट रूप से दो वास्तविक शून्यक देते हैं।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=-(x-3)(x+1)) है तो ग्राफ के शून्यक कौन से हैं?

If (p(x)=-(x-3)(x+1)), what are the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (3) और (-1)(3) and (-1)

Step 1

Concept

The outside negative sign does not change the zeroes. Set the factors equal to zero.

Step 2

Why this answer is correct

The correct answer is A. (3) और (-1) / (3) and (-1). The outside negative sign does not change the zeroes. Set the factors equal to zero.

Step 3

Exam Tip

बाहर का ऋण चिह्न शून्यकों को नहीं बदलता। गुणनखंडों को शून्य रखकर उत्तर निकालें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

किसी बहुपद के ग्राफ में (y)-अक्ष से प्रतिच्छेद ((0,-8)) है। इससे शून्यक के बारे में कौन सा निष्कर्ष सही है?

A polynomial graph has (y)-intercept ((0,-8)). Which conclusion about zeroes is correct?

Explanation opens after your attempt

Correct Answer

A. इससे शून्यक निश्चित नहीं होताA zero cannot be determined from this alone

Step 1

Concept

The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.

Step 2

Why this answer is correct

The correct answer is A. इससे शून्यक निश्चित नहीं होता / A zero cannot be determined from this alone. The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.

Step 3

Exam Tip

(y)-प्रतिच्छेद (p(0)) बताता है न कि सभी शून्यक। शून्यक के लिए (x)-अक्ष से प्रतिच्छेद चाहिए।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद के ग्राफ के (x)-प्रतिच्छेद ((-4,0)), ((1,0)), और ((6,0)) हैं तो शून्यकों का समुच्चय क्या है?

If the (x)-intercepts of a polynomial graph are ((-4,0)), ((1,0)), and ((6,0)), what is the set of zeroes?

Explanation opens after your attempt

Correct Answer

A. ({-4,1,6})

Step 1

Concept

A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.

Step 2

Why this answer is correct

The correct answer is A. ({-4,1,6}). A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.

Step 3

Exam Tip

शून्यक प्रतिच्छेद बिंदु का (x)-निर्देशांक होता है। (y=0) को शून्यक न लिखें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी ग्राफ के (x)-अक्ष कटान ((-4,0)), ((6,0)), ((16,0)) हैं, तो इनके शून्यकों का माध्य क्या है?

If the (x)-axis intersections of a graph are ((-4,0)), ((6,0)), ((16,0)), what is the mean of their zeroes?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.

Step 2

Why this answer is correct

The correct answer is A. (6). The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.

Step 3

Exam Tip

माध्य \(\frac{-4+6+16}{3}=6\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x)-अक्ष को ((-10,0)) और ((22,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?

If a graph cuts the (x)-axis at ((-10,0)) and ((22,0)), what change is needed to make the zeroes equally distant from the (y)-axis?

Explanation opens after your attempt

Correct Answer

A. (22) को (10) करना होगा(22) must be changed to (10)

Step 1

Concept

For equal distance from the (y)-axis, zeroes should be opposites, so (10) is needed with (-10). Tip: symmetric zeroes are (a) and (-a).

Step 2

Why this answer is correct

The correct answer is A. (22) को (10) करना होगा / (22) must be changed to (10). For equal distance from the (y)-axis, zeroes should be opposites, so (10) is needed with (-10). Tip: symmetric zeroes are (a) and (-a).

Step 3

Exam Tip

(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-10) के साथ (10) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?

If (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0), how many of the given (x)-values are zeroes?

Explanation opens after your attempt

Correct Answer

B. तीनThree

Step 1

Concept

The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.

Step 2

Why this answer is correct

The correct answer is B. तीन / Three. The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.

Step 3

Exam Tip

(-12), (4), (15) पर फलन मान (0) है। टिप: (p(-2)=6) को शून्यक न मानें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि नीचे खुलने वाले परवलय के शून्यक (-5) और (13) हैं, तो (x=2) पर ग्राफ कहाँ होगा?

If a downward-opening parabola has zeroes (-5) and (13), where will the graph be at (x=2)?

Explanation opens after your attempt

Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.

Step 3

Exam Tip

नीचे खुलने वाले परवलय में दो शून्यकों के बीच मान धनात्मक होते हैं। टिप: (x=2) दोनों शून्यकों के बीच है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-3-12x^-2+35x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?

If (p(x)=x^-3-12x^-2+35x), what is the set of zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (0,5,7)

Step 1

Concept

(x^-3-12x^-2+35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.

Step 2

Why this answer is correct

The correct answer is A. (0,5,7). (x^-3-12x^-2+35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.

Step 3

Exam Tip

(x^-3-12x^-2+35x=x(x-5)(x-7)) है, इसलिए शून्यक (0), (5), (7) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x=-12) और (x=12) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?

If a graph cuts the (x)-axis at (x=-12) and (x=12), what are the product and sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. गुणनफल (-144), योग (0)Product (-144), sum (0)

Step 1

Concept

The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 2

Why this answer is correct

The correct answer is A. गुणनफल (-144), योग (0) / Product (-144), sum (0). The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 3

Exam Tip

शून्यक (-12) और (12) हैं, इसलिए गुणनफल (-144) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि परवलय के शून्यक (q-11) और (q+7) हैं, तो सममिति अक्ष कौन सा होगा?

If the zeroes of a parabola are (q-11) and (q+7), what will be its axis of symmetry?

Explanation opens after your attempt

Correct Answer

A. (x=q-2)

Step 1

Concept

The axis of symmetry is at the average of the zeroes, (\frac{(q-11)+(q+7)}{2}=q-2). Tip: take the midpoint even with symbols.

Step 2

Why this answer is correct

The correct answer is A. (x=q-2). The axis of symmetry is at the average of the zeroes, (\frac{(q-11)+(q+7)}{2}=q-2). Tip: take the midpoint even with symbols.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के औसत पर है, (\frac{(q-11)+(q+7)}{2}=q-2)। टिप: प्रतीकों में भी मध्य मान लें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि कोई ग्राफ (y)-अक्ष को मूल बिंदु पर काटता है और (x=-9) पर (x)-अक्ष को काटता है, तो शून्यक कौन से हैं?

If a graph cuts the (y)-axis at the origin and cuts the (x)-axis at (x=-9), what are the zeroes?

Explanation opens after your attempt

Correct Answer

A. (0) और (-9)(0) and (-9)

Step 1

Concept

The origin is also on the (x)-axis, and (x=-9) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).

Step 2

Why this answer is correct

The correct answer is A. (0) और (-9) / (0) and (-9). The origin is also on the (x)-axis, and (x=-9) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).

Step 3

Exam Tip

मूल बिंदु (x)-अक्ष पर भी है और (x=-9) भी (x)-अक्ष कटान है। टिप: ((0,0)) को शून्यक (0) के रूप में गिनें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x=-18), (x=-6), (x=5) और (x=13) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?

If a graph cuts the (x)-axis at (x=-18), (x=-6), (x=5), and (x=13), what is the range of the zeroes?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

The range is the difference between the greatest and smallest zero, (13-(-18)=31). Tip: range is always non-negative.

Step 2

Why this answer is correct

The correct answer is C. (31). The range is the difference between the greatest and smallest zero, (13-(-18)=31). Tip: range is always non-negative.

Step 3

Exam Tip

परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है (13-(-18)=31)। टिप: परास हमेशा गैरऋणात्मक होती है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-c)⁵(x+d)²), जहाँ \(c\neq -d\), तो अलग शून्यक कौन से हैं?

If (p(x)=(x-c)⁵(x+d)²), where \(c\neq -d\), what are the distinct zeroes?

Explanation opens after your attempt

Correct Answer

A. (c) और (-d)(c) and (-d)

Step 1

Concept

From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (c) और (-d) / (c) and (-d). From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.

Step 3

Exam Tip

(x-c=0) से (c) और (x+d=0) से (-d) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x+2)⁶(x-5)²) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?

If (p(x)=(x+2)⁶(x-5)²), what are the number of distinct real zeroes and graph behavior?

Explanation opens after your attempt

Correct Answer

A. दो, दोनों पर स्पर्शTwo, touches at both

Step 1

Concept

There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.

Step 2

Why this answer is correct

The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.

Step 3

Exam Tip

दो अलग शून्यक (-2) और (5) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-3-9x^-2+18x) है, तो ग्राफ के शून्यकों का माध्य क्या है?

If (p(x)=x^-3-9x^-2+18x), what is the mean of the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.

Step 2

Why this answer is correct

The correct answer is A. (3). (p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.

Step 3

Exam Tip

(p(x)=x(x-3)(x-6)) है इसलिए शून्यक (0), (3), (6) और माध्य (3) है। टिप: पहले गुणनखंड करें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?

If (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0), what is the distance between the given zeroes?

Explanation opens after your attempt

Correct Answer

A. (11)

Step 1

Concept

The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).

Step 2

Why this answer is correct

The correct answer is A. (11). The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).

Step 3

Exam Tip

दिए गए शून्यक (-7) और (4) हैं इसलिए दूरी (4-(-7)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

एक ऊपर खुलने वाले परवलय के शून्यक (-9) और (3) हैं। (x=-4) पर ग्राफ की स्थिति क्या होगी?

An upward-opening parabola has zeroes (-9) and (3). What will be the position of the graph at (x=-4)?

Explanation opens after your attempt

Correct Answer

A. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

(x=-4) lies between the two zeroes and an upward-opening parabola stays below there. Tip: check the sign region between zeroes.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-4) lies between the two zeroes and an upward-opening parabola stays below there. Tip: check the sign region between zeroes.

Step 3

Exam Tip

(x=-4) दोनों शून्यकों के बीच है और ऊपर खुलने वाला परवलय बीच में नीचे रहता है। टिप: शून्यकों के बीच संकेत क्षेत्र देखें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी ग्राफ के (x)-अक्ष कटान ((-3,0)), ((5,0)), ((13,0)) हैं, तो इनके शून्यकों का माध्य क्या है?

If the (x)-axis intersections of a graph are ((-3,0)), ((5,0)), ((13,0)), what is the mean of their zeroes?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

The mean is \(\frac{-3+5+13}{3}=5\). Tip: first read the (x)-values from intersection points.

Step 2

Why this answer is correct

The correct answer is A. (5). The mean is \(\frac{-3+5+13}{3}=5\). Tip: first read the (x)-values from intersection points.

Step 3

Exam Tip

माध्य \(\frac{-3+5+13}{3}=5\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x)-अक्ष को ((-8,0)) और ((18,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?

If a graph cuts the (x)-axis at ((-8,0)) and ((18,0)), what change is needed to make the zeroes equally distant from the (y)-axis?

Explanation opens after your attempt

Correct Answer

A. (18) को (8) करना होगा(18) must be changed to (8)

Step 1

Concept

For equal distance from the (y)-axis, zeroes should be opposites, so (8) is needed with (-8). Tip: symmetric zeroes are (a) and (-a).

Step 2

Why this answer is correct

The correct answer is A. (18) को (8) करना होगा / (18) must be changed to (8). For equal distance from the (y)-axis, zeroes should be opposites, so (8) is needed with (-8). Tip: symmetric zeroes are (a) and (-a).

Step 3

Exam Tip

(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-8) के साथ (8) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?

If (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0), how many of the given (x)-values are zeroes?

Explanation opens after your attempt

Correct Answer

B. तीनThree

Step 1

Concept

The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.

Step 2

Why this answer is correct

The correct answer is B. तीन / Three. The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.

Step 3

Exam Tip

(-10), (3), (12) पर फलन मान (0) है। टिप: (p(-1)=4) को शून्यक न मानें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि नीचे खुलने वाले परवलय के शून्यक (-3) और (11) हैं, तो (x=4) पर ग्राफ कहाँ होगा?

If a downward-opening parabola has zeroes (-3) and (11), where will the graph be at (x=4)?

Explanation opens after your attempt

Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=4) lies between the zeroes.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=4) lies between the zeroes.

Step 3

Exam Tip

नीचे खुलने वाले परवलय में दो शून्यकों के बीच मान धनात्मक होते हैं। टिप: (x=4) दोनों शून्यकों के बीच है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-3-10x^-2+24x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?

If (p(x)=x^-3-10x^-2+24x), what is the set of zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (0,4,6)

Step 1

Concept

(x^-3-10x^-2+24x=x(x-4)(x-6)), so the zeroes are (0), (4), (6). Tip: first take (x) as the common factor.

Step 2

Why this answer is correct

The correct answer is A. (0,4,6). (x^-3-10x^-2+24x=x(x-4)(x-6)), so the zeroes are (0), (4), (6). Tip: first take (x) as the common factor.

Step 3

Exam Tip

(x^-3-10x^-2+24x=x(x-4)(x-6)) है, इसलिए शून्यक (0), (4), (6) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x=-10) और (x=10) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?

If a graph cuts the (x)-axis at (x=-10) and (x=10), what are the product and sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. गुणनफल (-100), योग (0)Product (-100), sum (0)

Step 1

Concept

The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 2

Why this answer is correct

The correct answer is A. गुणनफल (-100), योग (0) / Product (-100), sum (0). The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).

Step 3

Exam Tip

शून्यक (-10) और (10) हैं, इसलिए गुणनफल (-100) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि परवलय के शून्यक (t-9) और (t+5) हैं, तो सममिति अक्ष कौन सा होगा?

If the zeroes of a parabola are (t-9) and (t+5), what will be its axis of symmetry?

Explanation opens after your attempt

Correct Answer

A. (x=t-2)

Step 1

Concept

The axis of symmetry is at the average of the zeroes, (\frac{(t-9)+(t+5)}{2}=t-2). Tip: take the midpoint even with symbols.

Step 2

Why this answer is correct

The correct answer is A. (x=t-2). The axis of symmetry is at the average of the zeroes, (\frac{(t-9)+(t+5)}{2}=t-2). Tip: take the midpoint even with symbols.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के औसत पर है, (\frac{(t-9)+(t+5)}{2}=t-2)। टिप: प्रतीकों में भी मध्य मान लें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि कोई ग्राफ (y)-अक्ष को मूल बिंदु पर काटता है और (x=6) पर (x)-अक्ष को काटता है, तो शून्यक कौन से हैं?

If a graph cuts the (y)-axis at the origin and cuts the (x)-axis at (x=6), what are the zeroes?

Explanation opens after your attempt

Correct Answer

A. (0) और (6)(0) and (6)

Step 1

Concept

The origin is also on the (x)-axis, and (x=6) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).

Step 2

Why this answer is correct

The correct answer is A. (0) और (6) / (0) and (6). The origin is also on the (x)-axis, and (x=6) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).

Step 3

Exam Tip

मूल बिंदु (x)-अक्ष पर भी है और (x=6) भी (x)-अक्ष कटान है। टिप: ((0,0)) को शून्यक (0) के रूप में गिनें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x=-15), (x=-5), (x=4) और (x=11) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?

If a graph cuts the (x)-axis at (x=-15), (x=-5), (x=4), and (x=11), what is the range of the zeroes?

Explanation opens after your attempt

Correct Answer

C. (26)

Step 1

Concept

The range is the difference between the greatest and smallest zero, (11-(-15)=26). Tip: range is always non-negative.

Step 2

Why this answer is correct

The correct answer is C. (26). The range is the difference between the greatest and smallest zero, (11-(-15)=26). Tip: range is always non-negative.

Step 3

Exam Tip

परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है, (11-(-15)=26)। टिप: परास हमेशा गैरऋणात्मक होती है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x+a)³(x-b)²), जहाँ \(a\neq -b\), तो अलग शून्यक कौन से हैं?

If (p(x)=(x+a)³(x-b)²), where \(a\neq -b\), what are the distinct zeroes?

Explanation opens after your attempt

Correct Answer

A. (-a) और (b)(-a) and (b)

Step 1

Concept

From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (-a) और (b) / (-a) and (b). From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.

Step 3

Exam Tip

(x+a=0) से (-a) और (x-b=0) से (b) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x-1)²(x+4)⁴) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?

If (p(x)=(x-1)²(x+4)⁴), what are the number of distinct real zeroes and graph behavior?

Explanation opens after your attempt

Correct Answer

A. दो, दोनों पर स्पर्शTwo, touches at both

Step 1

Concept

There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.

Step 2

Why this answer is correct

The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.

Step 3

Exam Tip

दो अलग शून्यक (1) और (-4) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x^-3-7x^-2+10x) है, तो ग्राफ के शून्यकों का माध्य क्या है?

If (p(x)=x^-3-7x^-2+10x), what is the mean of the zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. \(\frac{7}{3}\)

Step 1

Concept

(p(x)=x(x-5)(x-2)), so the zeroes are (0), (2), (5), and the mean is \(\frac{7}{3}\). Tip: factor first.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{7}{3}\). (p(x)=x(x-5)(x-2)), so the zeroes are (0), (2), (5), and the mean is \(\frac{7}{3}\). Tip: factor first.

Step 3

Exam Tip

(p(x)=x(x-5)(x-2)) है, इसलिए शून्यक (0), (2), (5) और माध्य \(\frac{7}{3}\) है। टिप: पहले गुणनखंड करें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?

If (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0), what is the distance between the given zeroes?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).

Step 2

Why this answer is correct

The correct answer is B. (11). The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).

Step 3

Exam Tip

दिए गए शून्यक (-6) और (5) हैं, इसलिए दूरी (5-(-6)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

एक ऊपर खुलने वाले परवलय के शून्यक (-4) और (10) हैं। (x=0) पर ग्राफ की स्थिति क्या होगी?

An upward-opening parabola has zeroes (-4) and (10). What will be the position of the graph at (x=0)?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

(0) lies between the two zeroes and an upward parabola stays below there. Tip: check the sign region between zeroes.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (0) lies between the two zeroes and an upward parabola stays below there. Tip: check the sign region between zeroes.

Step 3

Exam Tip

(0) दोनों शून्यकों के बीच है और ऊपर खुलने वाला परवलय बीच में नीचे रहता है। टिप: शून्यकों के बीच संकेत क्षेत्र देखें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी ग्राफ के (x)-अक्ष कटान ((-2,0)), ((4,0)), ((10,0)) हैं तो इनके शून्यकों का माध्य क्या है?

If the (x)-axis intersections of a graph are ((-2,0)), ((4,0)), ((10,0)), what is the mean of their zeroes?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The mean is \(\frac{-2+4+10}{3}=4\). Tip: first read the (x)-values from intersection points.

Step 2

Why this answer is correct

The correct answer is A. (4). The mean is \(\frac{-2+4+10}{3}=4\). Tip: first read the (x)-values from intersection points.

Step 3

Exam Tip

माध्य \(\frac{-2+4+10}{3}=4\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((-6,0)) और ((14,0)) पर काटता है तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?

If a graph cuts the (x)-axis at ((-6,0)) and ((14,0)), what change is needed to make the zeroes equally distant from the (y)-axis?

Explanation opens after your attempt

Correct Answer

A. (14) को (6) करना होगा(14) must be changed to (6)

Step 1

Concept

For equal distance from the (y)-axis, zeroes should be opposites, so (6) is needed with (-6). Tip: symmetric zeroes are (a) and (-a).

Step 2

Why this answer is correct

The correct answer is A. (14) को (6) करना होगा / (14) must be changed to (6). For equal distance from the (y)-axis, zeroes should be opposites, so (6) is needed with (-6). Tip: symmetric zeroes are (a) and (-a).

Step 3

Exam Tip

(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-6) के साथ (6) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0) है तो कितने दिए गए (x)-मान शून्यक हैं?

If (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0), how many of the given (x)-values are zeroes?

Explanation opens after your attempt

Correct Answer

B. तीनThree

Step 1

Concept

The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.

Step 2

Why this answer is correct

The correct answer is B. तीन / Three. The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.

Step 3

Exam Tip

(-9), (2), (6) पर फलन मान (0) है। टिप: (p(-4)=2) को शून्यक न मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x)-अक्ष को ((7,0)) पर छूता है और ((-4,0)) पर काटता है तो शून्यकों का योग क्या है?

If a graph touches the (x)-axis at ((7,0)) and crosses it at ((-4,0)), what is the sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.

Step 2

Why this answer is correct

The correct answer is A. (3). The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.

Step 3

Exam Tip

शून्यक (7) और (-4) हैं इसलिए योग (3) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x^-3-8x^-2+15x) है तो ग्राफ के शून्यकों का समूह कौन सा है?

If (p(x)=x^-3-8x^-2+15x), what is the set of zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (0,3,5)

Step 1

Concept

(x^-3-8x^-2+15x=x(x-3)(x-5)), so the zeroes are (0,3,5). Tip: first take (x) as the common factor.

Step 2

Why this answer is correct

The correct answer is A. (0,3,5). (x^-3-8x^-2+15x=x(x-3)(x-5)), so the zeroes are (0,3,5). Tip: first take (x) as the common factor.

Step 3

Exam Tip

(x^-3-8x^-2+15x=x(x-3)(x-5)) है इसलिए शून्यक (0,3,5) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (x)-अक्ष से मिलने वाले बिंदु ((-5,0)), ((-5,0)), ((4,0)) लिखे हैं तो अलग वास्तविक शून्यक कितने हैं?

If the points meeting the (x)-axis are written as ((-5,0)), ((-5,0)), ((4,0)), how many distinct real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. ((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.

Step 3

Exam Tip

((-5,0)) दोहराया गया है इसलिए अलग शून्यक (-5) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ के शून्यक (-6), (2), (9) हैं तो (x)-अक्ष कटान बिंदुओं का सही समूह कौन सा है?

If the zeroes of a graph are (-6), (2), (9), which is the correct set of (x)-axis intersection points?

Explanation opens after your attempt

Correct Answer

B. ((-6,0)), ((2,0)), ((9,0))

Step 1

Concept

A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.

Step 2

Why this answer is correct

The correct answer is B. ((-6,0)), ((2,0)), ((9,0)). A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.

Step 3

Exam Tip

शून्यक (r) का बिंदु ((r,0)) होता है। टिप: शून्यक को पहले निर्देशांक में लिखें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि परवलय के शून्यक (c-7) और (c+3) हैं तो सममिति अक्ष कौन सा होगा?

If the zeroes of a parabola are (c-7) and (c+3), what will be its axis of symmetry?

Explanation opens after your attempt

Correct Answer

A. (x=c-2)

Step 1

Concept

The axis of symmetry is at the average of the zeroes, (\frac{(c-7)+(c+3)}{2}=c-2). Tip: the average rule also works with symbols.

Step 2

Why this answer is correct

The correct answer is A. (x=c-2). The axis of symmetry is at the average of the zeroes, (\frac{(c-7)+(c+3)}{2}=c-2). Tip: the average rule also works with symbols.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के औसत पर है (\frac{(c-7)+(c+3)}{2}=c-2)। टिप: प्रतीकों में भी औसत का नियम लागू होता है।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ के (x)-अक्ष कटान ((m,0)), ((n,0)), ((r,0)) हैं तो शून्यकों का माध्य क्या होगा?

If the (x)-axis intersections of a graph are ((m,0)), ((n,0)), ((r,0)), what will be the mean of the zeroes?

Explanation opens after your attempt

Correct Answer

B. \(\frac{m+n+r}{3}\)

Step 1

Concept

The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{m+n+r}{3}\). The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.

Step 3

Exam Tip

शून्यक (m), (n), (r) हैं इसलिए माध्य \(\frac{m+n+r}{3}\) है। टिप: प्रतीकात्मक बिंदुओं में भी पहला निर्देशांक लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि ग्राफ (x=-12), (x=-3), (x=8) पर (x)-अक्ष को काटता है तो शून्यकों की परास क्या है?

If a graph cuts the (x)-axis at (x=-12), (x=-3), (x=8), what is the range of the zeroes?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

The range is the difference between the greatest and smallest zero, (8-(-12)=20). Tip: range is not negative.

Step 2

Why this answer is correct

The correct answer is C. (20). The range is the difference between the greatest and smallest zero, (8-(-12)=20). Tip: range is not negative.

Step 3

Exam Tip

परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है (8-(-12)=20)। टिप: परास ऋणात्मक नहीं होती।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x-4)(x+7)³) है तो अलग शून्यक कौन से हैं?

If (p(x)=(x-4)(x+7)³), what are the distinct zeroes?

Explanation opens after your attempt

Correct Answer

A. (4) और (-7)(4) and (-7)

Step 1

Concept

The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (4) और (-7) / (4) and (-7). The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.

Step 3

Exam Tip

शून्यक (4) और (-7) हैं पर (-7) दोहराया गया है। टिप: अलग शून्यक में दोहराव को एक बार गिनें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(-8)=0), (p(-2)>0), (p(3)=0) और (p(9)<0) है तो दिए गए शून्यकों का योग क्या है?

If (p(-8)=0), (p(-2)>0), (p(3)=0) and (p(9)<0), what is the sum of the given zeroes?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).

Step 2

Why this answer is correct

The correct answer is A. (-5). The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).

Step 3

Exam Tip

दिए गए शून्यक (-8) और (3) हैं इसलिए योग (-5) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि परवलय के शून्यक (-7) और (5) हैं तथा वह ऊपर की ओर खुलता है तो (x=-1) पर ग्राफ कहाँ होगा?

If a parabola has zeroes (-7) and (5) and opens upward, where will the graph be at (x=-1)?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

(x=-1) lies between the zeroes and an upward-opening parabola is below the axis there. Tip: check the sign region between zeroes.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-1) lies between the zeroes and an upward-opening parabola is below the axis there. Tip: check the sign region between zeroes.

Step 3

Exam Tip

(x=-1) दोनों शून्यकों के बीच है और ऊपर खुलने वाले परवलय में बीच का भाग नीचे होता है। टिप: शून्यकों के बीच संकेत क्षेत्र देखें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी ग्राफ के (x)-अक्ष कटान ((-1,0)), ((3,0)), ((7,0)) हैं, तो इनके शून्यकों का माध्य क्या है?

If the (x)-axis intersections of a graph are ((-1,0)), ((3,0)), ((7,0)), what is the mean of their zeroes?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The mean is \(\frac{-1+3+7}{3}=3\). Tip: first read the (x)-values from intersection points.

Step 2

Why this answer is correct

The correct answer is A. (3). The mean is \(\frac{-1+3+7}{3}=3\). Tip: first read the (x)-values from intersection points.

Step 3

Exam Tip

माध्य \(\frac{-1+3+7}{3}=3\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x)-अक्ष को ((-4,0)) और ((10,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?

If a graph cuts the (x)-axis at ((-4,0)) and ((10,0)), what change is needed to make the zeroes equally distant from the (y)-axis?

Explanation opens after your attempt

Correct Answer

A. (10) को (4) करना होगा(10) must be changed to (4)

Step 1

Concept

For equal distance from the (y)-axis, zeroes should be opposites, so (4) is needed with (-4). Tip: symmetric zeroes are (a) and (-a).

Step 2

Why this answer is correct

The correct answer is A. (10) को (4) करना होगा / (10) must be changed to (4). For equal distance from the (y)-axis, zeroes should be opposites, so (4) is needed with (-4). Tip: symmetric zeroes are (a) and (-a).

Step 3

Exam Tip

(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-4) के साथ (4) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), तो कितने दिए गए (x)-मान शून्यक हैं?

If (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), how many of the given (x)-values are zeroes?

Explanation opens after your attempt

Correct Answer

B. तीनThree

Step 1

Concept

The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.

Step 2

Why this answer is correct

The correct answer is B. तीन / Three. The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.

Step 3

Exam Tip

(-7), (1), (4) पर फलन मान (0) है। टिप: (p(-3)=2) को शून्यक न मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x)-अक्ष को ((5,0)) पर छूता है और ((-3,0)) पर काटता है, तो शून्यकों का योग क्या है?

If a graph touches the (x)-axis at ((5,0)) and crosses it at ((-3,0)), what is the sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.

Step 2

Why this answer is correct

The correct answer is A. (2). The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.

Step 3

Exam Tip

शून्यक (5) और (-3) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x^-3-6x^-2+5x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?

If (p(x)=x^-3-6x^-2+5x), what is the set of zeroes of the graph?

Explanation opens after your attempt

Correct Answer

A. (0,1,5)

Step 1

Concept

(x^-3-6x^-2+5x=x(x-1)(x-5)), so the zeroes are (0,1,5). Tip: first take (x) as the common factor.

Step 2

Why this answer is correct

The correct answer is A. (0,1,5). (x^-3-6x^-2+5x=x(x-1)(x-5)), so the zeroes are (0,1,5). Tip: first take (x) as the common factor.

Step 3

Exam Tip

(x^-3-6x^-2+5x=x(x-1)(x-5)) है, इसलिए शून्यक (0,1,5) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (x)-अक्ष से मिलने वाले बिंदु ((2,0)), ((2,0)), ((9,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?

If the points meeting the (x)-axis are written as ((2,0)), ((2,0)), ((9,0)), how many distinct real zeroes are there?

Explanation opens after your attempt

Correct Answer

B. दोTwo

Step 1

Concept

((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. ((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.

Step 3

Exam Tip

((2,0)) दोहराया गया है, इसलिए अलग शून्यक (2) और (9) हैं। टिप: समान (x)-मान को एक बार गिनें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ के शून्यक (-4), (1), (8) हैं, तो (x)-अक्ष कटान बिंदुओं का सही समूह कौन सा है?

If the zeroes of a graph are (-4), (1), (8), which is the correct set of (x)-axis intersection points?

Explanation opens after your attempt

Correct Answer

B. ((-4,0)), ((1,0)), ((8,0))

Step 1

Concept

A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.

Step 2

Why this answer is correct

The correct answer is B. ((-4,0)), ((1,0)), ((8,0)). A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.

Step 3

Exam Tip

शून्यक (r) का बिंदु ((r,0)) होता है। टिप: शून्यक को पहले निर्देशांक में लिखें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि परवलय के शून्यक (b-5) और (b+1) हैं, तो सममिति अक्ष कौन सा होगा?

If the zeroes of a parabola are (b-5) and (b+1), what will be its axis of symmetry?

Explanation opens after your attempt

Correct Answer

A. (x=b-2)

Step 1

Concept

The axis of symmetry is at the average of the zeroes, (\frac{(b-5)+(b+1)}{2}=b-2). Tip: the average rule also works with symbols.

Step 2

Why this answer is correct

The correct answer is A. (x=b-2). The axis of symmetry is at the average of the zeroes, (\frac{(b-5)+(b+1)}{2}=b-2). Tip: the average rule also works with symbols.

Step 3

Exam Tip

सममिति अक्ष शून्यकों के औसत पर है, (\frac{(b-5)+(b+1)}{2}=b-2)। टिप: प्रतीकों में भी औसत का नियम लागू होता है।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि ग्राफ (x=-10), (x=-4), (x=6) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?

If a graph cuts the (x)-axis at (x=-10), (x=-4), (x=6), what is the range of the zeroes?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

The range is the difference between the greatest and smallest zero, (6-(-10)=16). Tip: range is not negative.

Step 2

Why this answer is correct

The correct answer is C. (16). The range is the difference between the greatest and smallest zero, (6-(-10)=16). Tip: range is not negative.

Step 3

Exam Tip

परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है, (6-(-10)=16)। टिप: परास ऋणात्मक नहीं होती।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-2)(x+6)³) है, तो अलग शून्यक कौन से हैं?

If (p(x)=(x-2)(x+6)³), what are the distinct zeroes?

Explanation opens after your attempt

Correct Answer

A. (2) और (-6)(2) and (-6)

Step 1

Concept

The zeroes are (2) and (-6), but (-6) is repeated. Tip: count repetition once for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (2) और (-6) / (2) and (-6). The zeroes are (2) and (-6), but (-6) is repeated. Tip: count repetition once for distinct zeroes.

Step 3

Exam Tip

शून्यक (2) और (-6) हैं, पर (-6) दोहराया गया है। टिप: अलग शून्यक में दोहराव एक बार गिनें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(-6)=0), (p(-1)>0), (p(4)=0) और (p(7)<0) है, तो दिए गए शून्यकों का गुणनफल क्या है?

If (p(-6)=0), (p(-1)>0), (p(4)=0) and (p(7)<0), what is the product of the given zeroes?

Explanation opens after your attempt

Correct Answer

A. (-24)

Step 1

Concept

The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).

Step 2

Why this answer is correct

The correct answer is A. (-24). The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).

Step 3

Exam Tip

दिए गए शून्यक (-6) और (4) हैं, इसलिए गुणनफल (-24) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी परवलय के शून्यक (-8) और (2) हैं तथा वह ऊपर की ओर खुलता है, तो (x=-3) पर ग्राफ कहाँ होगा?

If a parabola has zeroes (-8) and (2) and opens upward, where will the graph be at (x=-3)?

Explanation opens after your attempt

Correct Answer

B. (x)-अक्ष के नीचेBelow the (x)-axis

Step 1

Concept

(x=-3) lies between the two zeroes, and an upward parabola is below the axis there. Tip: check the sign between zeroes.

Step 2

Why this answer is correct

The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-3) lies between the two zeroes, and an upward parabola is below the axis there. Tip: check the sign between zeroes.

Step 3

Exam Tip

(x=-3) दोनों शून्यकों के बीच है और ऊपर खुलने वाले परवलय में बीच का भाग नीचे होता है। टिप: शून्यकों के बीच संकेत देखें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि ग्राफ (x)-अक्ष को ((-3,0)) और ((9,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?

If a graph cuts the (x)-axis at ((-3,0)) and ((9,0)), what change is needed to make the zeroes equally distant from the (y)-axis?

Explanation opens after your attempt

Correct Answer

A. (9) को (3) करना होगा(9) must be changed to (3)

Step 1

Concept

For equal distance from the (y)-axis, zeroes should be opposites, so (3) is needed with (-3). Tip: symmetric zeroes are (a) and (-a).

Step 2

Why this answer is correct

The correct answer is A. (9) को (3) करना होगा / (9) must be changed to (3). For equal distance from the (y)-axis, zeroes should be opposites, so (3) is needed with (-3). Tip: symmetric zeroes are (a) and (-a).

Step 3

Exam Tip

(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-3) के साथ (3) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी ग्राफ में (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), तो कितने दिए गए (x)-मान शून्यक हैं?

If in a graph (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), how many of the given (x)-values are zeroes?

Explanation opens after your attempt

Correct Answer

B. तीनThree

Step 1

Concept

The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.

Step 2

Why this answer is correct

The correct answer is B. तीन / Three. The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.

Step 3

Exam Tip

(-4), (2), (5) पर फलन मान (0) है। टिप: (p(0)=3) को शून्यक न मानें।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी ग्राफ का (x)-अक्ष से एक स्पर्श ((4,0)) पर है और एक कटान ((-2,0)) पर है, तो शून्यकों का योग क्या है?

If a graph touches the (x)-axis at ((4,0)) and crosses it at ((-2,0)), what is the sum of the zeroes?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.

Step 2

Why this answer is correct

The correct answer is A. (2). The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.

Step 3

Exam Tip

शून्यक (4) और (-2) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।

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यदि द्विघात ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटता है तो उसके वास्तविक शून्यक कैसे होंगे?

Concept

Why this answer is correct

Exam Tip

किस स्थिति में द्विघात बहुपद के दो वास्तविक शून्यक होंगे?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को ((2,0)) और ((7,0)) पर काटता है, तो शून्यक कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

यदि परवलय (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है, तो द्विघात बहुपद के कितने शून्यक होंगे?

Concept

Why this answer is correct

Exam Tip

यदि परवलय के शून्यक (-4) और (10) हैं तथा वह नीचे की ओर खुलता है तो शून्यकों के बाहर ग्राफ कहाँ होगा?

Concept

Why this answer is correct

Exam Tip

यदि परवलय के शून्यक (-2) और (8) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?

Concept

Why this answer is correct

Exam Tip

यदि किसी परवलय के शून्यक (-1) और (7) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?

Concept

Why this answer is correct

Exam Tip

यदि किसी बहुपद के वास्तविक शून्यक (5), (5), (-1) हैं तो अलग वास्तविक शून्यक कौन से हैं?

Concept

Why this answer is correct

Exam Tip

यदि किसी बहुपद के वास्तविक शून्यक (2), (2) और (-5) लिखे हैं, तो अलग वास्तविक शून्यक कौन से हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात बहुपद (p(x)) का ग्राफ (x)-अक्ष को (-2) और (5) पर काटता है तो उसके शून्यकों की संख्या क्या है?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात बहुपद के वास्तविक शून्यक (1) और (4) हैं तो उसका आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-2dx+d-2-36) है, तो ग्राफ के शून्यक कौन से होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-19x+90) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-2cx+c-2-25) है, तो ग्राफ के शून्यक कौन से होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-17x+72) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-2bx+b-2-16) है तो ग्राफ के शून्यक कौन से होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-15x+56) है तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-2ax+a-2-9) है, तो ग्राफ के शून्यक कौन से होंगे?

Concept

Why this answer is correct

यदि (p(x)=x^-2-6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?

यदि (p(x)=x^-2-2dx+d^-2-36) है, तो ग्राफ के शून्यक कौन से होंगे?

यदि (p(x)=x^-2-19x+90) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

यदि (p(x)=x^-2-2cx+c^-2-25) है, तो ग्राफ के शून्यक कौन से होंगे?

यदि (p(x)=x^-2-17x+72) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

यदि (p(x)=x^-2-2bx+b^-2-16) है तो ग्राफ के शून्यक कौन से होंगे?

यदि (p(x)=x^-2-15x+56) है तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

यदि (p(x)=x^-2-2ax+a^-2-9) है, तो ग्राफ के शून्यक कौन से होंगे?

यदि (p(x)=x^-2-13x+42) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

यदि (p(x)=x^-2-11x+30) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?

यदि (p(x)=x^-2+x-6) है तो वास्तविक शून्यक कौन से हैं?

यदि (p(x)=2x^-2-8) है तो ग्राफ के शून्यक कौन से हैं?

यदि (p(x)=-x^-2+25), तो ग्राफ के वास्तविक शून्यक कौन से होंगे?