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Mathematics Quiz - Class 10 Mathematics Expert Level 48 Quiz

Question 1/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-5x^-2+ax+12) में (x-3) गुणनखंड है, तो (a) का मान क्या है?

If (x-3) is a factor of (p(x)=x^-3-5x^-2+ax+12), what is the value of (a)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

By the factor theorem (p(3)=0), so (27-45+3a+12=0) and (a=2). In exams, substitute the zero from the given factor directly.

Step 2

Why this answer is correct

The correct answer is A. (2). By the factor theorem (p(3)=0), so (27-45+3a+12=0) and (a=2). In exams, substitute the zero from the given factor directly.

Step 3

Exam Tip

गुणनखंड प्रमेय से (p(3)=0), इसलिए (27-45+3a+12=0) और (a=2)। परीक्षा में दिए गए गुणनखंड से मूल तुरंत रखिए।

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Question 2/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=2x^-3+kx^-2-11x+5) को (x+1) से भाग देने पर शेष (7) है, तो (k) क्या है?

If (p(x)=2x^-3+kx^-2-11x+5) leaves remainder (7) when divided by (x+1), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (-9)

Step 1

Concept

By the remainder theorem (p(-1)=7), so (-2+k+11+5=7). This gives (k=-7), so none of the listed options is correct.

Step 2

Why this answer is correct

The correct answer is B. (-9). By the remainder theorem (p(-1)=7), so (-2+k+11+5=7). This gives (k=-7), so none of the listed options is correct.

Step 3

Exam Tip

शेष प्रमेय से (p(-1)=7), इसलिए (-2+k+11+5=7)। इससे (k=-7) नहीं बल्कि (k=-7) आता है, इसलिए विकल्पों में सही मान नहीं है।

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Question 3/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-(m+4)x+4m) के शून्यक (4) और (m) हैं, तो कौन-सा कथन सही है?

If the zeroes of (p(x)=x^-2-(m+4)x+4m) are (4) and (m), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. यह हर वास्तविक (m) के लिए सही हैIt is true for every real (m)

Step 1

Concept

The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).

Step 2

Why this answer is correct

The correct answer is A. यह हर वास्तविक (m) के लिए सही है / It is true for every real (m). The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).

Step 3

Exam Tip

योग (4+m) और गुणनफल (4m) हैं, जो दिए बहुपद से मिलते हैं। इसलिए कथन हर वास्तविक (m) के लिए सही है।

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Question 4/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+rx+9) के दोनों शून्यक समान और ऋणात्मक हैं, तो (r) का मान क्या होगा?

If both zeroes of (p(x)=x^-2+rx+9) are equal and negative, what is the value of (r)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

For equal zeroes, \(r^2-36=0\), so \(r=\pm6\). For negative zeroes the sum must be positive (6), hence (r=6).

Step 2

Why this answer is correct

The correct answer is A. (6). For equal zeroes, \(r^2-36=0\), so \(r=\pm6\). For negative zeroes the sum must be positive (6), hence (r=6).

Step 3

Exam Tip

समान शून्यकों के लिए \(r^2-36=0\), अतः \(r=\pm6\)। ऋणात्मक शून्यक के लिए योग धनात्मक (6) होना चाहिए, इसलिए (r=6)।

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Question 5/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि \(\alpha\) और \(\beta\), \(3x^2-10x+7\) के शून्यक हैं, तो \(\alpha^2+\beta^2\) का मान क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(3x^2-10x+7\), what is the value of \(\alpha^2+\beta^2\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{58}{9}\)

Step 1

Concept

Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{58}{9}\). Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).

Step 3

Exam Tip

यहाँ \(\alpha+\beta=\frac{10}{3}\) और \(\alpha\beta=\frac{7}{3}\) हैं। इसलिए (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9})।

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Question 6/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-2x^-2-13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?

If (p(x)=x^-3-2x^-2-13x-10), which of the following is a zero of (p(x))?

Explanation opens after your attempt

Correct Answer

D. -(2)

Step 1

Concept

(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.

Step 2

Why this answer is correct

The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.

Step 3

Exam Tip

(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।

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Question 7/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (x=2) और (x=-3), (p(x)=ax^-2+bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?

If (x=2) and (x=-3) are zeroes of (p(x)=ax^-2+bx+c), what is \(\frac{c}{a}\)?

Explanation opens after your attempt

Correct Answer

A. -(6)

Step 1

Concept

The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.

Step 2

Why this answer is correct

The correct answer is A. -(6). The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.

Step 3

Exam Tip

शून्यकों का गुणनफल (2\cdot(-3)=-6) है और यह \(\frac{c}{a}\) के बराबर होता है। गुणनफल में संकेत पर विशेष ध्यान दें।

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Question 8/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-6x+s) का एक शून्यक दूसरे से (2) अधिक है, तो (s) का मान क्या है?

If one zero of (p(x)=x^-2-6x+s) is (2) more than the other, what is (s)?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

Let the zeroes be (t) and (t+2), then (2t+2=6) gives (t=2). The product is \(2\cdot4=8\), so (s=8).

Step 2

Why this answer is correct

The correct answer is A. (8). Let the zeroes be (t) and (t+2), then (2t+2=6) gives (t=2). The product is \(2\cdot4=8\), so (s=8).

Step 3

Exam Tip

शून्यक (t) और (t+2) मानें, तो (2t+2=6) से (t=2)। गुणनफल \(2\cdot4=8\), इसलिए (s=8)।

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Question 9/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=2x^-2-5x-3), तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

If (p(x)=2x^-2-5x-3), what is \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\), where \(\alpha,\beta\) are zeroes?

Explanation opens after your attempt

Correct Answer

A. -\(\frac{37}{6}\)

Step 1

Concept

\(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=-\frac{3}{2}\). (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)²-2\alpha\beta}{\alpha\beta}=-\frac{37}{6}).

Step 2

Why this answer is correct

The correct answer is A. -\(\frac{37}{6}\). \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=-\frac{3}{2}\). (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)²-2\alpha\beta}{\alpha\beta}=-\frac{37}{6}).

Step 3

Exam Tip

\(\alpha+\beta=\frac{5}{2}\) और \(\alpha\beta=-\frac{3}{2}\) हैं। (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)²-2\alpha\beta}{\alpha\beta}=-\frac{37}{6})।

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Question 10/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-4x^-2-7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?

If (p(x)=x^-3-4x^-2-7x+10) and (x-1) is a factor, what is the remaining quadratic factor?

Explanation opens after your attempt

Correct Answer

A. \(x^2-3x-10\)

Step 1

Concept

Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x-10\). Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).

Step 3

Exam Tip

(p(x)) को (x-1) से भाग देने पर \(x^2-3x-10\) मिलता है। गुणा करके जाँचें कि ((x-1)\(x^2-3x-10\)=p(x))।

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Question 11/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=(k-3)x^-5+2x^-3-x+9) की घात (3) है, तो (k) क्या है?

If (p(x)=(k-3)x^-5+2x^-3-x+9) has degree (3), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).

Step 2

Why this answer is correct

The correct answer is A. (3). For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).

Step 3

Exam Tip

घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए। इसलिए (k-3=0) और (k=3)।

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Question 12/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि \(\alpha,\beta\), \(x^2-9x+20\) के शून्यक हैं, तो (\(\alpha+2\)\(\beta+2\)) का मान क्या है?

If \(\alpha,\beta\) are zeroes of \(x^2-9x+20\), what is the value of (\(\alpha+2\)\(\beta+2\))?

Explanation opens after your attempt

Correct Answer

A. (42)

Step 1

Concept

\(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).

Step 2

Why this answer is correct

The correct answer is A. (42). \(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).

Step 3

Exam Tip

\(\alpha+\beta=9\) और \(\alpha\beta=20\) हैं। (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42)।

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Question 13/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?

If (p(x)=x^-2-4x+1), what is the sum of reciprocals of its zeroes?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).

Step 3

Exam Tip

शून्यकों के व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=1\), इसलिए उत्तर (4) है।

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Question 14/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि किसी द्विघात बहुपद के शून्यक \(2+\sqrt{3}\) और \(2-\sqrt{3}\) हैं, तो मोनिक बहुपद कौन-सा है?

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+1\). The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).

Step 3

Exam Tip

योग (4) और गुणनफल (1) है। अतः मोनिक बहुपद \(x^2-4x+1\) होगा।

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Question 15/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-6x^-2+12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?

If (p(x)=x^-3-6x^-2+12x-8), what is the zero of (p(x)) with its multiplicity?

Explanation opens after your attempt

Correct Answer

A. (2) गुणनता (3)(2) with multiplicity (3)

Step 1

Concept

This is (p(x)=(x-2)³), so (2) is a zero three times. Recognizing cube identities is useful.

Step 2

Why this answer is correct

The correct answer is A. (2) गुणनता (3) / (2) with multiplicity (3). This is (p(x)=(x-2)³), so (2) is a zero three times. Recognizing cube identities is useful.

Step 3

Exam Tip

यह (p(x)=(x-2)³) है, इसलिए (2) तीन बार शून्यक है। घन पूर्ण पहचान को पहचानना उपयोगी है।

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Question 16/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=3x^-2-12x+15), तो वास्तविक शून्यकों के बारे में सही निष्कर्ष क्या है?

For (p(x)=3x^-2-12x+15), what is the correct conclusion about real zeroes?

Explanation opens after your attempt

Correct Answer

A. कोई वास्तविक शून्यक नहींNo real zeroes

Step 1

Concept

(p(x)=3\(x^2-4x+5\)=3((x-2)²+1)), which is always positive. Hence there are no real zeroes.

Step 2

Why this answer is correct

The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zeroes. (p(x)=3\(x^2-4x+5\)=3((x-2)²+1)), which is always positive. Hence there are no real zeroes.

Step 3

Exam Tip

(p(x)=3\(x^2-4x+5\)=3((x-2)²+1)), जो सदा धनात्मक है। इसलिए कोई वास्तविक शून्यक नहीं है।

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Question 17/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+bx+16) के शून्यक परस्पर व्युत्क्रम हैं, तो (b) के बारे में क्या कहा जा सकता है?

If the zeroes of (p(x)=x^-2+bx+16) are reciprocals of each other, what can be said about (b)?

Explanation opens after your attempt

Correct Answer

A. ऐसा संभव नहीं हैIt is not possible

Step 1

Concept

Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.

Step 2

Why this answer is correct

The correct answer is A. ऐसा संभव नहीं है / It is not possible. Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.

Step 3

Exam Tip

परस्पर व्युत्क्रम शून्यकों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (16) है, इसलिए यह संभव नहीं है।

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Question 18/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-11x+30) और (q(x)=p(x-2)), तो (q(x)) के शून्यक कौन-से हैं?

If (p(x)=x^-2-11x+30) and (q(x)=p(x-2)), what are the zeroes of (q(x))?

Explanation opens after your attempt

Correct Answer

A. (7,8)

Step 1

Concept

The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).

Step 2

Why this answer is correct

The correct answer is A. (7,8). The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).

Step 3

Exam Tip

(p(x)) के शून्यक (5) और (6) हैं। (p(x-2)=0) के लिए (x-2=5) या (x-2=6), इसलिए शून्यक (7,8) हैं।

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Question 19/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-3x-28), तो (p(x)) के शून्यकों के मध्य दूरी क्या है?

If (p(x)=x^-2-3x-28), what is the distance between its zeroes?

Explanation opens after your attempt

Correct Answer

A. (11)

Step 1

Concept

(p(x)=(x-7)(x+4)), so the zeroes are (7) and (-4). The distance is (|7-(-4)|=11).

Step 2

Why this answer is correct

The correct answer is A. (11). (p(x)=(x-7)(x+4)), so the zeroes are (7) and (-4). The distance is (|7-(-4)|=11).

Step 3

Exam Tip

(p(x)=(x-7)(x+4)), इसलिए शून्यक (7) और (-4) हैं। दूरी (|7-(-4)|=11) है।

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Question 20/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=2x^-2+mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?

If one zero of (p(x)=2x^-2+mx+18) is (3), what is the other zero?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).

Step 2

Why this answer is correct

The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).

Step 3

Exam Tip

गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।

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Question 21/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=4x^-2-4x+1), तो इसके शून्यक क्या हैं?

If (p(x)=4x^-2-4x+1), what are its zeroes?

Explanation opens after your attempt

Correct Answer

A. \(\frac{1}{2},\frac{1}{2}\)

Step 1

Concept

(4x^-2-4x+1=(2x-1)²), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{2},\frac{1}{2}\). (4x^-2-4x+1=(2x-1)²), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.

Step 3

Exam Tip

(4x^-2-4x+1=(2x-1)²), इसलिए शून्यक \(\frac{1}{2}\) दो बार है। पूर्ण वर्ग रूप तुरंत समान शून्यक देता है।

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Question 22/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-4-5x^-2+4), तो इसके वास्तविक शून्यक कौन-से हैं?

If (p(x)=x^-4-5x^-2+4), what are its real zeroes?

Explanation opens after your attempt

Correct Answer

A. -(2,-1,1,2)

Step 1

Concept

(x^-4-5x^-2+4=\(x^2-1\)\(x^2-4\)). Therefore the real zeroes are (-2,-1,1,2).

Step 2

Why this answer is correct

The correct answer is A. -(2,-1,1,2). (x^-4-5x^-2+4=\(x^2-1\)\(x^2-4\)). Therefore the real zeroes are (-2,-1,1,2).

Step 3

Exam Tip

(x^-4-5x^-2+4=\(x^2-1\)\(x^2-4\)) है। इसलिए वास्तविक शून्यक (-2,-1,1,2) हैं।

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Question 23/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3+ax^-2+bx-12) के शून्यक (1,3,-4) हैं, तो (a+b) क्या है?

If the zeroes of (p(x)=x^-3+ax^-2+bx-12) are (1,3,-4), what is (a+b)?

Explanation opens after your attempt

Correct Answer

A. -(9)

Step 1

Concept

The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).

Step 2

Why this answer is correct

The correct answer is A. -(9). The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).

Step 3

Exam Tip

योग (1+3-4=0) है, इसलिए (a=0)। युग्म गुणनफलों का योग (3-4-12=-13), इसलिए (b=-13) और (a+b=-13)।

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Question 24/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?

If (p(x)=x^-3-9x), how many distinct real zeroes does it have?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(x^-3-9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.

Step 2

Why this answer is correct

The correct answer is A. (3). (x^-3-9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.

Step 3

Exam Tip

(x^-3-9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं।

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Question 25/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-2x-8), तो (p(x+3)) के शून्यक कौन-से हैं?

If (p(x)=x^-2-2x-8), what are the zeroes of (p(x+3))?

Explanation opens after your attempt

Correct Answer

A. -(5,1)

Step 1

Concept

The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).

Step 2

Why this answer is correct

The correct answer is A. -(5,1). The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).

Step 3

Exam Tip

(p(x)) के शून्यक (4) और (-2) हैं। (x+3=4) या (x+3=-2) से शून्यक (1) और (-5) मिलते हैं।

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Question 26/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-5x+6), तो (p(2)+p(3)) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).

Step 2

Why this answer is correct

The correct answer is A. (0). (2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).

Step 3

Exam Tip

(2) और (3), (p(x)) के शून्यक हैं, इसलिए (p(2)=0) और (p(3)=0)। इसलिए योग (0) है।

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Question 27/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=ax^-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

If (p(x)=ax^-2+bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (p(x)) शून्य बहुपद है(p(x)) is the zero polynomial

Step 1

Concept

A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 2

Why this answer is correct

The correct answer is A. (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial. A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 3

Exam Tip

अधिकतम द्विघात बहुपद के तीन अलग-अलग शून्यक तभी हो सकते हैं जब वह शून्य बहुपद हो। घात से अधिक अलग शून्यक असंभव होते हैं।

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Question 28/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?

If the zeroes of (p(x)=x^-2-kx+36) are positive and in the ratio (1:4), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).

Step 2

Why this answer is correct

The correct answer is A. (15). Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).

Step 3

Exam Tip

शून्यक (t) और (4t) मानें, तो \(4t^2=36\) से (t=3) है। योग (15) है, इसलिए (k=15)।

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Question 29/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=2x^-2-7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?

If (p(x)=2x^-2-7x+5), what is the difference between the sum and product of its zeroes?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).

Step 2

Why this answer is correct

The correct answer is A. (1). The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).

Step 3

Exam Tip

योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है।

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Question 30/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (x=2) पर (p(x)=x^-3+mx-10) का मान (0) है, तो (m) क्या है?

If the value of (p(x)=x^-3+mx-10) at (x=2) is (0), what is (m)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(p(2)=8+2m-10=0). This gives (2m=2) and (m=1).

Step 2

Why this answer is correct

The correct answer is A. (1). (p(2)=8+2m-10=0). This gives (2m=2) and (m=1).

Step 3

Exam Tip

(p(2)=8+2m-10=0) है। इससे (2m=2) और (m=1) मिलता है।

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Question 31/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+4x+4), तो (p(-2+h)) का मान क्या है?

If (p(x)=x^-2+4x+4), what is the value of (p(-2+h))?

Explanation opens after your attempt

Correct Answer

A. \(h^2\)

Step 1

Concept

(p(x)=(x+2)²), so (p(-2+h)=h^-2). Perfect square form makes substitution easier.

Step 2

Why this answer is correct

The correct answer is A. \(h^2\). (p(x)=(x+2)²), so (p(-2+h)=h^-2). Perfect square form makes substitution easier.

Step 3

Exam Tip

(p(x)=(x+2)²), इसलिए (p(-2+h)=h^-2)। पूर्ण वर्ग रूप से प्रतिस्थापन आसान हो जाता है।

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Question 32/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3+px^-2+qx+15) के शून्यक (-1,3,-5) हैं, तो (p+q) क्या है?

If the zeroes of (p(x)=x^-3+px^-2+qx+15) are (-1,3,-5), what is (p+q)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).

Step 2

Why this answer is correct

The correct answer is B. (2). The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).

Step 3

Exam Tip

शून्यकों का योग (-3) है, इसलिए (p=3)। युग्म गुणनफलों का योग (-3+5-15=-13), इसलिए (q=-13) और (p+q=-10)।

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Question 33/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-12x+35), तो \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

If (p(x)=x^-2-12x+35), what is \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\), where \(\alpha,\beta\) are zeroes?

Explanation opens after your attempt

Correct Answer

D. \(\frac{11}{24}\)

Step 1

Concept

\(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).

Step 2

Why this answer is correct

The correct answer is D. \(\frac{11}{24}\). \(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).

Step 3

Exam Tip

\(\alpha+\beta=12\) और \(\alpha\beta=35\) हैं। \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\)।

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Question 34/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+2x-24), तो (p(x)) का कौन-सा गुणनखंड है?

If (p(x)=x^-2+2x-24), which is a factor of (p(x))?

Explanation opens after your attempt

Correct Answer

A. (x-4)

Step 1

Concept

(x^-2+2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.

Step 2

Why this answer is correct

The correct answer is A. (x-4). (x^-2+2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.

Step 3

Exam Tip

(x^-2+2x-24=(x-4)(x+6)) है। इसलिए (x-4) एक गुणनखंड है।

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Question 35/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=5x^-2-20x+20), तो इसके शून्यकों का योग क्या है?

If (p(x)=5x^-2-20x+20), what is the sum of its zeroes?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.

Step 2

Why this answer is correct

The correct answer is A. (4). The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.

Step 3

Exam Tip

योग \(-\frac{b}{a}=-\frac{-20}{5}=4\) है। पहले सामान्य गुणनखंड निकालना चाहें तो भी योग वही रहेगा।

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Question 36/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-4-16), तो \(x^2+4\) के कारण वास्तविक शून्यकों पर क्या प्रभाव पड़ता है?

For (p(x)=x^-4-16), what effect does \(x^2+4\) have on real zeroes?

Explanation opens after your attempt

Correct Answer

A. यह कोई वास्तविक शून्यक नहीं देताIt gives no real zero

Step 1

Concept

(x^-4-16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).

Step 2

Why this answer is correct

The correct answer is A. यह कोई वास्तविक शून्यक नहीं देता / It gives no real zero. (x^-4-16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).

Step 3

Exam Tip

(x^-4-16=\(x^2-4\)\(x^2+4\)) है। \(x^2+4\) वास्तविक (x) के लिए कभी (0) नहीं होता।

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Question 37/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+ax+a) में (p(1)=0), तो (a) क्या है?

If (p(x)=x^-2+ax+a) and (p(1)=0), what is (a)?

Explanation opens after your attempt

Correct Answer

A. -\(\frac{1}{2}\)

Step 1

Concept

(p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. -\(\frac{1}{2}\). (p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).

Step 3

Exam Tip

(p(1)=1+a+a=0), इसलिए (2a=-1)। अतः \(a=-\frac{1}{2}\) है।

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Question 38/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?

If the minimum value of (p(x)=x^-2-2x+k) is (3), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(x^-2-2x+k=(x-1)²+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 2

Why this answer is correct

The correct answer is A. (4). (x^-2-2x+k=(x-1)²+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 3

Exam Tip

(x^-2-2x+k=(x-1)²+k-1), इसलिए न्यूनतम मान (k-1) है। (k-1=3) से (k=4)।

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Question 39/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-4x+3) है, तो कौन-सा मान (p(x)<0) बनाता है?

If (p(x)=x^-2-4x+3), which value makes (p(x)<0)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

(p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.

Step 2

Why this answer is correct

The correct answer is A. (2). (p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.

Step 3

Exam Tip

(p(x)=(x-1)(x-3)) है और (1<x<3) में मान ऋणात्मक होता है। इसलिए (x=2) सही है।

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Question 40/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-3x^-2-4x+12), तो पूर्ण गुणनखंड रूप क्या है?

If (p(x)=x^-3-3x^-2-4x+12), what is the complete factor form?

Explanation opens after your attempt

Correct Answer

A. ((x-3)(x-2)(x+2))

Step 1

Concept

By grouping, (x^-2(x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).

Step 2

Why this answer is correct

The correct answer is A. ((x-3)(x-2)(x+2)). By grouping, (x^-2(x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).

Step 3

Exam Tip

समूहीकरण से (x^-2(x-3)-4(x-3)=(x-3)\(x^2-4\)) मिलता है। इसलिए गुणनखंड ((x-3)(x-2)(x+2)) हैं।

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Question 41/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+5x+6) और (r(x)=p(-x)), तो (r(x)) के शून्यक कौन-से हैं?

If (p(x)=x^-2+5x+6) and (r(x)=p(-x)), what are the zeroes of (r(x))?

Explanation opens after your attempt

Correct Answer

A. (2,3)

Step 1

Concept

The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).

Step 2

Why this answer is correct

The correct answer is A. (2,3). The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).

Step 3

Exam Tip

(p(x)) के शून्यक (-2) और (-3) हैं। (p(-x)=0) के लिए (-x=-2) या (-x=-3), इसलिए (x=2,3)।

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Question 42/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-7x+12) है, तो (p(x)) का ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?

If (p(x)=x^-2-7x+12), at which points will the graph of (p(x)) cut the (x)-axis?

Explanation opens after your attempt

Correct Answer

A. ((3,0),(4,0))

Step 1

Concept

(x^-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).

Step 2

Why this answer is correct

The correct answer is A. ((3,0),(4,0)). (x^-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).

Step 3

Exam Tip

(x^-2-7x+12=(x-3)(x-4)), इसलिए शून्यक (3) और (4) हैं। (x)-अक्ष पर बिंदु ((3,0)) और ((4,0)) होंगे।

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Question 43/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+2x+c) का कोई वास्तविक शून्यक नहीं है, तो (c) के लिए कौन-सी शर्त सही है?

If (p(x)=x^-2+2x+c) has no real zero, which condition on (c) is correct?

Explanation opens after your attempt

Correct Answer

A. (c>1)

Step 1

Concept

For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).

Step 2

Why this answer is correct

The correct answer is A. (c>1). For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).

Step 3

Exam Tip

कोई वास्तविक शून्यक नहीं होने के लिए विविक्तकर (4-4c<0) चाहिए। इससे (c>1) मिलता है।

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Question 44/50 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 45/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=2x^-2+x-6), तो (2p(1)-p(-2)) का मान क्या है?

If (p(x)=2x^-2+x-6), what is the value of (2p(1)-p(-2))?

Explanation opens after your attempt

Correct Answer

A. -(6)

Step 1

Concept

(p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).

Step 2

Why this answer is correct

The correct answer is A. -(6). (p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).

Step 3

Exam Tip

(p(1)=2+1-6=-3) और (p(-2)=8-2-6=0)। इसलिए (2p(1)-p(-2)=-6)।

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Question 46/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2+px+q) और (p(1)=0,\ p(2)=0), तो (p+q) क्या है?

If (p(x)=x^-2+px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?

Explanation opens after your attempt

Correct Answer

A. -(1)

Step 1

Concept

The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).

Step 2

Why this answer is correct

The correct answer is A. -(1). The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).

Step 3

Exam Tip

शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)।

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Question 47/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-ax+b) के शून्यक (a) और (b) हैं, तो कौन-सा संबंध सही है?

If the zeroes of (p(x)=x^-2-ax+b) are (a) and (b), which relation is correct?

Explanation opens after your attempt

Correct Answer

A. (a+b=a) और (ab=b)(a+b=a) and (ab=b)

Step 1

Concept

The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).

Step 2

Why this answer is correct

The correct answer is A. (a+b=a) और (ab=b) / (a+b=a) and (ab=b). The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).

Step 3

Exam Tip

शून्यकों का योग बहुपद से (a) और गुणनफल (b) है। इसलिए यदि शून्यक (a,b) हैं, तो (a+b=a) और (ab=b) होना चाहिए।

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Question 48/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-3-1), तो निम्न में से कौन-सा रैखिक गुणनखंड है?

If (p(x)=x^-3-1), which of the following is a linear factor?

Explanation opens after your attempt

Correct Answer

A. (x-1)

Step 1

Concept

(x^-3-1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.

Step 2

Why this answer is correct

The correct answer is A. (x-1). (x^-3-1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.

Step 3

Exam Tip

(x^-3-1=(x-1)\(x^2+x+1\)) है। इसलिए (x-1) रैखिक गुणनखंड है।

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Question 49/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-8x+16) है, तो (p(4+t)) का मान क्या है?

If (p(x)=x^-2-8x+16), what is the value of (p(4+t))?

Explanation opens after your attempt

Correct Answer

A. \(t^2\)

Step 1

Concept

(p(x)=(x-4)²), so (p(4+t)=t^-2). In such questions, first form a perfect square.

Step 2

Why this answer is correct

The correct answer is A. \(t^2\). (p(x)=(x-4)²), so (p(4+t)=t^-2). In such questions, first form a perfect square.

Step 3

Exam Tip

(p(x)=(x-4)²), इसलिए (p(4+t)=t^-2)। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।

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Question 50/50 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-4x+6), तो (p(x+1)-p(x)) का मान क्या है?

If (p(x)=x^-2-4x+6), what is the value of (p(x+1)-p(x))?

Explanation opens after your attempt

Correct Answer

A. (2x-3)

Step 1

Concept

(p(x+1)=x^-2-2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.

Step 2

Why this answer is correct

The correct answer is A. (2x-3). (p(x+1)=x^-2-2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.

Step 3

Exam Tip

(p(x+1)=x^-2-2x+3) और (p(x+1)-p(x)=2x-3) है। ऐसे प्रश्नों में पहले (x+1) को सावधानी से प्रतिस्थापित करें।

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Class 10 Mathematics Expert Quiz

यदि (p(x)=x-3-5x-2+ax+12) में (x-3) गुणनखंड है, तो (a) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=2x-3+kx-2-11x+5) को (x+1) से भाग देने पर शेष (7) है, तो (k) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-(m+4)x+4m) के शून्यक (4) और (m) हैं, तो कौन-सा कथन सही है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2+rx+9) के दोनों शून्यक समान और ऋणात्मक हैं, तो (r) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(\alpha\) और \(\beta\), \(3x^2-10x+7\) के शून्यक हैं, तो \(\alpha^2+\beta^2\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-3-2x-2-13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?

Concept

Why this answer is correct

Exam Tip

यदि (x=2) और (x=-3), (p(x)=ax-2+bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-6x+s) का एक शून्यक दूसरे से (2) अधिक है, तो (s) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=2x-2-5x-3), तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-3-4x-2-7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=(k-3)x-5+2x-3-x+9) की घात (3) है, तो (k) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(\alpha,\beta\), \(x^2-9x+20\) के शून्यक हैं, तो (\(\alpha+2\)\(\beta+2\)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात बहुपद के शून्यक \(2+\sqrt{3}\) और \(2-\sqrt{3}\) हैं, तो मोनिक बहुपद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-3-6x-2+12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=3x-2-12x+15), तो वास्तविक शून्यकों के बारे में सही निष्कर्ष क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2+bx+16) के शून्यक परस्पर व्युत्क्रम हैं, तो (b) के बारे में क्या कहा जा सकता है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-11x+30) और (q(x)=p(x-2)), तो (q(x)) के शून्यक कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-3x-28), तो (p(x)) के शून्यकों के मध्य दूरी क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=2x-2+mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?

Concept

Why this answer is correct

यदि (p(x)=x^-3-5x^-2+ax+12) में (x-3) गुणनखंड है, तो (a) का मान क्या है?

यदि (p(x)=2x^-3+kx^-2-11x+5) को (x+1) से भाग देने पर शेष (7) है, तो (k) क्या है?

यदि (p(x)=x^-2-(m+4)x+4m) के शून्यक (4) और (m) हैं, तो कौन-सा कथन सही है?

यदि (p(x)=x^-2+rx+9) के दोनों शून्यक समान और ऋणात्मक हैं, तो (r) का मान क्या होगा?

यदि (p(x)=x^-3-2x^-2-13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?

यदि (x=2) और (x=-3), (p(x)=ax^-2+bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?

यदि (p(x)=x^-2-6x+s) का एक शून्यक दूसरे से (2) अधिक है, तो (s) का मान क्या है?

यदि (p(x)=2x^-2-5x-3), तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

यदि (p(x)=x^-3-4x^-2-7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?

यदि (p(x)=(k-3)x^-5+2x^-3-x+9) की घात (3) है, तो (k) क्या है?

यदि (p(x)=x^-2-4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?

यदि (p(x)=x^-3-6x^-2+12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?

यदि (p(x)=3x^-2-12x+15), तो वास्तविक शून्यकों के बारे में सही निष्कर्ष क्या है?

यदि (p(x)=x^-2+bx+16) के शून्यक परस्पर व्युत्क्रम हैं, तो (b) के बारे में क्या कहा जा सकता है?

यदि (p(x)=x^-2-11x+30) और (q(x)=p(x-2)), तो (q(x)) के शून्यक कौन-से हैं?

यदि (p(x)=x^-2-3x-28), तो (p(x)) के शून्यकों के मध्य दूरी क्या है?

यदि (p(x)=2x^-2+mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?

यदि (p(x)=4x^-2-4x+1), तो इसके शून्यक क्या हैं?

यदि (p(x)=x^-4-5x^-2+4), तो इसके वास्तविक शून्यक कौन-से हैं?

यदि (p(x)=x^-3+ax^-2+bx-12) के शून्यक (1,3,-4) हैं, तो (a+b) क्या है?

यदि (p(x)=x^-3-9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?

यदि (p(x)=x^-2-2x-8), तो (p(x+3)) के शून्यक कौन-से हैं?

यदि (p(x)=x^-2-5x+6), तो (p(2)+p(3)) का मान क्या है?

यदि (p(x)=ax^-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

यदि (p(x)=x^-2-kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?

यदि (p(x)=2x^-2-7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?

यदि (x=2) पर (p(x)=x^-3+mx-10) का मान (0) है, तो (m) क्या है?

यदि (p(x)=x^-2+4x+4), तो (p(-2+h)) का मान क्या है?

यदि (p(x)=x^-3+px^-2+qx+15) के शून्यक (-1,3,-5) हैं, तो (p+q) क्या है?

यदि (p(x)=x^-2-12x+35), तो \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

यदि (p(x)=x^-2+2x-24), तो (p(x)) का कौन-सा गुणनखंड है?

यदि (p(x)=5x^-2-20x+20), तो इसके शून्यकों का योग क्या है?

यदि (p(x)=x^-4-16), तो \(x^2+4\) के कारण वास्तविक शून्यकों पर क्या प्रभाव पड़ता है?

यदि (p(x)=x^-2+ax+a) में (p(1)=0), तो (a) क्या है?

यदि (p(x)=x^-2-2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?