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13 results found for "distinct-real-zeroes" in Class 10.

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

यदि किसी परवलय का शीर्ष ((-14,0)) है और वह नीचे की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?

If the vertex of a parabola is ((-14,0)) and it opens downward, how many distinct real zeroes are there?

Explanation opens after your attempt
Correct Answer

B. एकOne

Step 1

Concept

The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.

Step 2

Why this answer is correct

The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((-14,0)). Tip: if the vertex has (y=0), there is one distinct zero.

Step 3

Exam Tip

शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((-14,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता 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)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 22

यदि किसी परवलय का शीर्ष ((12,0)) है और वह ऊपर की ओर खुलता है, तो अलग वास्तविक शून्यक कितने हैं?

If the vertex of a parabola is ((12,0)) and it opens upward, how many distinct real zeroes are there?

Explanation opens after your attempt
Correct Answer

B. एकOne

Step 1

Concept

The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.

Step 2

Why this answer is correct

The correct answer is B. एक / One. The vertex lies on the (x)-axis, so the parabola touches at ((12,0)). Tip: if the vertex has (y=0), there is one distinct zero.

Step 3

Exam Tip

शीर्ष (x)-अक्ष पर है, इसलिए परवलय ((12,0)) पर स्पर्श करेगा। टिप: शीर्ष का (y)-मान (0) हो तो एक अलग शून्यक होता 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-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 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 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 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 24

किस ग्राफ से ठीक दो अलग वास्तविक शून्यक मिलेंगे?

Which graph will give exactly two distinct real zeroes?

Explanation opens after your attempt
Correct Answer

A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटेOne that cuts the (x)-axis at two distinct points

Step 1

Concept

Two distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections as zeroes.

Step 2

Why this answer is correct

The correct answer is A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points. Two distinct (x)-axis intersections give two distinct real zeroes. Tip: do not count (y)-axis intersections as zeroes.

Step 3

Exam Tip

दो अलग (x)-अक्ष कटान दो अलग वास्तविक शून्यक देते हैं। टिप: (y)-अक्ष कटान को शून्यक न गिनें।

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

यदि किसी ग्राफ में (x=1) पर कटान और (x=6) पर स्पर्श है तो अलग वास्तविक शून्यक कितने हैं?

If a graph crosses at (x=1) and touches at (x=6), how many distinct real zeroes are there?

Explanation opens after your attempt
Correct Answer

B. दोTwo

Step 1

Concept

Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Both crossing and touching show (p(x)=0). Tip: count the distinct (x)-values.

Step 3

Exam Tip

कटान और स्पर्श दोनों (p(x)=0) बताते हैं। टिप: अलग (x)-मानों को गिनें।

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

यदि किसी बहुपद का आलेख ((2,0)) पर स्पर्श करता है और ((5,0)) पर काटता है तो अलग वास्तविक शून्यक कितने हैं?

If a polynomial graph touches at ((2,0)) and crosses at ((5,0)), how many distinct real zeroes are there?

Explanation opens after your attempt
Correct Answer

B. दोTwo

Step 1

Concept

Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.

Step 2

Why this answer is correct

The correct answer is B. दो / Two. Both touching and crossing show meeting the (x)-axis. Tip: count distinct (x)-values.

Step 3

Exam Tip

स्पर्श और कटान दोनों (x)-अक्ष से मिलना दिखाते हैं। टिप: अलग (x)-मान गिनें।

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

परवलय (x)-अक्ष को ((2,0)) और ((2,0)) पर ही छूता है। अलग वास्तविक शून्यकों की संख्या क्या है?

A parabola touches the (x)-axis only at ((2,0)). What is the number of distinct real zeroes?

Explanation opens after your attempt
Correct Answer

A. एकOne

Step 1

Concept

For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. एक / One. For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.

Step 3

Exam Tip

दोहराया शून्यक होने पर अलग (x)-मान केवल (2) है। टिप: अलग शून्यक गिनते समय समान बिंदु दो बार न गिनें।

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

यदि ग्राफ (x)-अक्ष को ((2,0)) पर काटता और ((5,0)) पर छूता है, तो अलग वास्तविक शून्यक कितने हैं?

If a graph cuts the (x)-axis at ((2,0)) and touches it at ((5,0)), how many distinct real zeroes are there?

Explanation opens after your attempt
Correct Answer

A. दोTwo

Step 1

Concept

Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो / Two. Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.

Step 3

Exam Tip

कटना और छूना दोनों (x)-अक्ष से मिलना है। दो अलग बिंदु हैं, इसलिए दो अलग वास्तविक शून्यक हैं।

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