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Class 10 Mathematics - Quadratic Equations - Roots of a Quadratic Equation Easy Quiz

Mathematics Quadratic Equations Roots of a Quadratic Equation Easy Class 10 Level 32

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Question 1/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किसी द्विघात समीकरण (p(x)=0) का मूल वह संख्या है जिससे (p(x)) का मान क्या हो जाता है?

A root of a quadratic equation (p(x)=0) is a number for which the value of (p(x)) becomes what?

Explanation opens after your attempt
Correct Answer

B. (0)

Explanation

Simple Explanation

मूल रखने पर (p(x)=0) बनता है। परीक्षा में मूल की जांच हमेशा प्रतिस्थापन से करें। / When a root is substituted, (p(x)=0) becomes true. In exams always check a root by substitution.

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Question 2/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

क्या (x=1) समीकरण \(x^2-3x+2=0\) का मूल है?

Is (x=1) a root of \(x^2-3x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. हाँYes

Explanation

Simple Explanation

(x=1) रखने पर (1-3+2=0) मिलता है। इसलिए (1) इसका मूल है। / Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.

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Question 3/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

क्या (x=-2) समीकरण \(x^2+3x+2=0\) का मूल है?

Is (x=-2) a root of \(x^2+3x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. हाँYes

Explanation

Simple Explanation

(x=-2) रखने पर (4-6+2=0) मिलता है। ऋणात्मक मान रखते समय चिन्हों पर ध्यान दें। / Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.

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Question 4/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-25=0\) के मूल कौन से हैं?

What are the roots of \(x^2-25=0\)?

Explanation opens after your attempt
Correct Answer

A. (5) और (-5)(5) and (-5)

Explanation

Simple Explanation

(x-2-25=(x-5)(x+5)) है। इसलिए मूल (5) और (-5) हैं। / (x-2-25=(x-5)(x+5)). Therefore the roots are (5) and (-5).

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Question 5/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-7x+12=0\) के मूल कौन से हैं?

What are the roots of \(x^2-7x+12=0\)?

Explanation opens after your attempt
Correct Answer

A. (3) और (4)(3) and (4)

Explanation

Simple Explanation

(x-2-7x+12=(x-3)(x-4)) है। इसलिए मूल (3) और (4) हैं। / (x-2-7x+12=(x-3)(x-4)). Therefore the roots are (3) and (4).

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Question 6/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+9x+20=0\) के मूल कौन से हैं?

What are the roots of \(x^2+9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. (-4) और (-5)(-4) and (-5)

Explanation

Simple Explanation

(x-2+9x+20=(x+4)(x+5)) है। इसलिए मूल (-4) और (-5) हैं। / (x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).

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Question 7/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (0) और (-6) हैं?

Which equation has roots (0) and (-6)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+6x=0\)

Explanation

Simple Explanation

मूल (0) और (-6) होने पर समीकरण (x(x+6)=0) होगा। इसे खोलने पर \(x^2+6x=0\) मिलता है। / With roots (0) and (-6), the equation is (x(x+6)=0). Expanding it gives \(x^2+6x=0\).

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Question 8/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (2) समीकरण \(x^2+qx-10=0\) का मूल है तो (q) का मान क्या है?

If (2) is a root of \(x^2+qx-10=0\), what is the value of (q)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

(x=2) रखने पर (4+2q-10=0) इसलिए (q=3)। दिए गए मूल को सीधे समीकरण में रखें। / Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.

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Question 9/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-5x+2=0\) के मूलों का योग क्या है?

What is the sum of roots of \(3x^2-5x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{5}{3}\)

Explanation

Simple Explanation

मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=3) और (b=-5) इसलिए योग \(\frac{5}{3}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=3) and (b=-5), so the sum is \(\frac{5}{3}\).

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Question 10/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(4x^2+7x-3=0\) के मूलों का गुणनफल क्या है?

What is the product of roots of \(4x^2+7x-3=0\)?

Explanation opens after your attempt
Correct Answer

B. \(-\frac{3}{4}\)

Explanation

Simple Explanation

मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{c}{a}=\frac{-3}{4}\) है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).

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Question 11/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (D>0) है तो द्विघात समीकरण के वास्तविक मूल कैसे होते हैं?

If (D>0), how are the real roots of a quadratic equation?

Explanation opens after your attempt
Correct Answer

B. दो भिन्न वास्तविक मूलTwo distinct real roots

Explanation

Simple Explanation

(D>0) होने पर दो भिन्न वास्तविक मूल मिलते हैं। मूलों की प्रकृति जानने के लिए \(D=b^2-4ac\) देखें। / When (D>0), two distinct real roots are obtained. To know the nature of roots, check \(D=b^2-4ac\).

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Question 12/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-2x+5=0\) का डिस्क्रिमिनेंट (D) क्या है?

What is the discriminant (D) of \(x^2-2x+5=0\)?

Explanation opens after your attempt
Correct Answer

C. (-16)

Explanation

Simple Explanation

यहां \(D=b^2-4ac=4-20=-16\) है। इसलिए वास्तविक मूल नहीं होंगे। / Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.

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Question 13/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस स्थिति में द्विघात समीकरण के कोई वास्तविक मूल नहीं होते?

In which condition does a quadratic equation have no real roots?

Explanation opens after your attempt
Correct Answer

C. (D<0)

Explanation

Simple Explanation

जब (D<0) होता है तब वास्तविक मूल नहीं होते। यह मूलों की प्रकृति का सीधा नियम है। / When (D<0), there are no real roots. This is a direct rule for the nature of roots.

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Question 14/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+9=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?

Which statement is correct about the real roots of \(x^2+9=0\)?

Explanation opens after your attempt
Correct Answer

C. कोई वास्तविक मूल नहीं हैIt has no real roots

Explanation

Simple Explanation

किसी वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+9=0\) वास्तविक संख्या से संतुष्ट नहीं होता। / For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.

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Question 15/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-5x=0\) के मूल कौन से हैं?

What are the roots of \(x^2-5x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0) और (5)(0) and (5)

Explanation

Simple Explanation

(x-2-5x=x(x-5)) है। इसलिए मूल (0) और (5) हैं। / (x-2-5x=x(x-5)). Therefore the roots are (0) and (5).

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Question 16/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2=9x\) के मूल कौन से हैं?

What are the roots of \(x^2=9x\)?

Explanation opens after your attempt
Correct Answer

A. (0) और (9)(0) and (9)

Explanation

Simple Explanation

\(x^2=9x\) को \(x^2-9x=0\) लिखें। फिर (x(x-9)=0) से मूल (0) और (9) मिलते हैं। / Write \(x^2=9x\) as \(x^2-9x=0\). Then (x(x-9)=0) gives roots (0) and (9).

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Question 17/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-27=0\) के मूल कौन से हैं?

What are the roots of \(3x^2-27=0\)?

Explanation opens after your attempt
Correct Answer

A. (3) और (-3)(3) and (-3)

Explanation

Simple Explanation

\(3x^2-27=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है। / From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).

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Question 18/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-8x+16=0\) का दोहराया हुआ मूल क्या है?

What is the repeated root of \(x^2-8x+16=0\)?

Explanation opens after your attempt
Correct Answer

A. (4)

Explanation

Simple Explanation

(x-2-8x+16=(x-4)2) है। इसलिए दोहराया हुआ मूल (4) है। / (x-2-8x+16=(x-4)2). Therefore the repeated root is (4).

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Question 19/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (-2) और (6) हैं?

Which equation has roots (-2) and (6)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-12=0\)

Explanation

Simple Explanation

मूल (-2) और (6) होने पर ((x+2)(x-6)=0) होगा। इसे खोलने पर \(x^2-4x-12=0\) मिलता है। / With roots (-2) and (6), we get ((x+2)(x-6)=0). Expanding it gives \(x^2-4x-12=0\).

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Question 20/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-9x+18=0\) का एक मूल (3) है तो दूसरा मूल क्या है?

If one root of \(x^2-9x+18=0\) is (3), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(x-2-9x+18=(x-3)(x-6)) है। इसलिए दूसरा मूल (6) है। / (x-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).

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Question 21/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि दो वास्तविक मूलों का गुणनफल धनात्मक और योग ऋणात्मक है तो दोनों मूल कैसे होंगे?

If the product of two real roots is positive and their sum is negative, how will both roots be?

Explanation opens after your attempt
Correct Answer

B. दोनों ऋणात्मकBoth negative

Explanation

Simple Explanation

गुणनफल धनात्मक होने पर दोनों मूलों का चिन्ह समान होता है। योग ऋणात्मक होने से दोनों मूल ऋणात्मक होंगे। / A positive product means both roots have the same sign. A negative sum means both roots are negative.

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Question 22/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (x+5) किसी द्विघात बहुपद का गुणनखंड है तो कौन सा मूल निश्चित होगा?

If (x+5) is a factor of a quadratic polynomial, which root is certain?

Explanation opens after your attempt
Correct Answer

B. (-5)

Explanation

Simple Explanation

(x+5=0) करने पर (x=-5) मिलता है। इसलिए निश्चित मूल (-5) है। / Solving (x+5=0) gives (x=-5). Therefore the certain root is (-5).

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Question 23/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (4) समीकरण \(x^2+mx-20=0\) का मूल है तो (m) का मान क्या है?

If (4) is a root of \(x^2+mx-20=0\), what is the value of (m)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(x=4) रखने पर (16+4m-20=0) इसलिए (m=1)। पैरामीटर के लिए मूल को सीधे रखें। / Putting (x=4) gives (16+4m-20=0), so (m=1). For a parameter, substitute the root directly.

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Question 24/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(7x^2=0\) के मूलों के बारे में सही कथन कौन सा है?

Which statement is correct about the roots of \(7x^2=0\)?

Explanation opens after your attempt
Correct Answer

A. (0) दोहराया हुआ मूल है(0) is a repeated root

Explanation

Simple Explanation

\(7x^2=0\) से \(x^2=0\) मिलता है। इसलिए (0) दोहराया हुआ मूल है। / From \(7x^2=0\), we get \(x^2=0\). Therefore (0) is a repeated root.

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Question 25/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-49=0\) के मूल कौन से हैं?

What are the roots of \(x^2-49=0\)?

Explanation opens after your attempt
Correct Answer

A. (7) और (-7)(7) and (-7)

Explanation

Simple Explanation

(x-2-49=(x-7)(x+7)) है। इसलिए मूल (7) और (-7) हैं। / (x-2-49=(x-7)(x+7)). Therefore the roots are (7) and (-7).

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Question 26/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

निम्न में से कौन सा मान \(x^2+4x=0\) का मूल है?

Which of the following values is a root of \(x^2+4x=0\)?

Explanation opens after your attempt
Correct Answer

B. (-4)

Explanation

Simple Explanation

(x-2+4x=x(x+4)) है। इसलिए मूल (0) और (-4) हैं। / (x-2+4x=x(x+4)). Therefore the roots are (0) and (-4).

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Question 27/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

किस समीकरण के मूल (5) और (-3) हैं?

Which equation has roots (5) and (-3)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2x-15=0\)

Explanation

Simple Explanation

मूल (5) और (-3) होने पर ((x-5)(x+3)=0) होगा। इसे खोलने पर \(x^2-2x-15=0\) मिलता है। / With roots (5) and (-3), we get ((x-5)(x+3)=0). Expanding it gives \(x^2-2x-15=0\).

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Question 28/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+11x+30=0\) के मूलों का योग क्या है?

What is the sum of roots of \(x^2+11x+30=0\)?

Explanation opens after your attempt
Correct Answer

B. (-11)

Explanation

Simple Explanation

मूलों का योग \(-\frac{b}{a}\) है। यहां योग (-11) होगा। / The sum of roots is \(-\frac{b}{a}\). Here the sum is (-11).

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Question 29/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(5x^2-2x-8=0\) के मूलों का गुणनफल क्या है?

What is the product of roots of \(5x^2-2x-8=0\)?

Explanation opens after your attempt
Correct Answer

C. \(-\frac{8}{5}\)

Explanation

Simple Explanation

मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-8}{5}\) सही है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.

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Question 30/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (0) समीकरण \(2x^2+bx+c=0\) का मूल है तो (c) का मान कैसा होगा?

If (0) is a root of \(2x^2+bx+c=0\), what must be the value of (c)?

Explanation opens after your attempt
Correct Answer

A. (c=0)

Explanation

Simple Explanation

(x=0) रखने पर (c=0) मिलना चाहिए। इसलिए शून्य मूल के लिए अचर पद शून्य होता है। / Putting (x=0) must give (c=0). Therefore the constant term is zero for a zero root.

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Question 31/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (-1) समीकरण \(x^2+rx-12=0\) का मूल है तो (r) का मान क्या है?

If (-1) is a root of \(x^2+rx-12=0\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

A. (-11)

Explanation

Simple Explanation

(x=-1) रखने पर (1-r-12=0) इसलिए (r=-11)। ऋणात्मक मूल रखते समय प्रत्येक पद का चिन्ह देखें। / Putting (x=-1) gives (1-r-12=0), so (r=-11). Check the sign of each term while using a negative root.

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Question 32/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+12x+36=0\) के मूल कौन से हैं?

What are the roots of \(x^2+12x+36=0\)?

Explanation opens after your attempt
Correct Answer

B. (-6) और (-6)(-6) and (-6)

Explanation

Simple Explanation

(x-2+12x+36=(x+6)2) है। इसलिए दोनों मूल (-6) हैं। / (x-2+12x+36=(x+6)2). Therefore both roots are (-6).

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Question 33/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(2x^2-10x=0\) के मूल कौन से हैं?

What are the roots of \(2x^2-10x=0\)?

Explanation opens after your attempt
Correct Answer

A. (0) और (5)(0) and (5)

Explanation

Simple Explanation

(2x-2-10x=2x(x-5)) है। इसलिए मूल (0) और (5) हैं। / (2x-2-10x=2x(x-5)). Therefore the roots are (0) and (5).

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Question 34/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+14x+49=0\) का मूल कौन सा है?

Which is the root of \(x^2+14x+49=0\)?

Explanation opens after your attempt
Correct Answer

B. (-7) दो बार(-7) twice

Explanation

Simple Explanation

(x-2+14x+49=(x+7)2) है। इसलिए दोहराया मूल (-7) है। / (x-2+14x+49=(x+7)2). Therefore the repeated root is (-7).

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Question 35/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

निम्न में से कौन सा मान \(x^2-64=0\) का मूल नहीं है?

Which of the following values is not a root of \(x^2-64=0\)?

Explanation opens after your attempt
Correct Answer

C. (0)

Explanation

Simple Explanation

\(x^2-64=0\) के मूल (8) और (-8) हैं। (0) रखने पर समीकरण सत्य नहीं होता। / The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.

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Question 36/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि ((x+1)(x-8)=0) है तो मूल कौन से होंगे?

If ((x+1)(x-8)=0), what are the roots?

Explanation opens after your attempt
Correct Answer

B. (-1) और (8)(-1) and (8)

Explanation

Simple Explanation

शून्य गुणनफल नियम से (x+1=0) या (x-8=0) होगा। इसलिए मूल (-1) और (8) हैं। / By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).

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Question 37/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी समीकरण के मूल (2) और (-5) हैं तो उनका योग क्या है?

If the roots of an equation are (2) and (-5), what is their sum?

Explanation opens after your attempt
Correct Answer

B. (-3)

Explanation

Simple Explanation

योग (2+(-5)=-3) है। ऋणात्मक मूल जोड़ते समय चिन्ह न भूलें। / The sum is (2+(-5)=-3). Do not forget the sign while adding a negative root.

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Question 38/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

जिस मोनिक द्विघात समीकरण के मूलों का योग (-9) और गुणनफल (20) है वह कौन सा है?

Which monic quadratic equation has sum of roots (-9) and product of roots (20)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+9x+20=0\)

Explanation

Simple Explanation

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। इसलिए \(x^2+9x+20=0\) सही है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)

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Question 39/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (2) समीकरण \(3x^2-8x+n=0\) का मूल है तो (n) का मान क्या है?

If (2) is a root of \(3x^2-8x+n=0\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

(x=2) रखने पर (12-16+n=0) इसलिए (n=4)। ऐसे प्रश्नों में गणना धीरे और सही करें। / Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.

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Question 40/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-5x+6=0\) के मूल कौन से हैं?

What are the roots of \(x^2-5x+6=0\)?

Explanation opens after your attempt
Correct Answer

A. (2) और (3)(2) and (3)

Explanation

Simple Explanation

(x-2-5x+6=(x-2)(x-3)) है। इसलिए मूल (2) और (3) हैं। / (x-2-5x+6=(x-2)(x-3)). Therefore the roots are (2) and (3).

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Question 41/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (-3) किसी द्विघात बहुपद का मूल है तो कौन सा गुणनखंड निश्चित होगा?

If (-3) is a root of a quadratic polynomial, which factor is certain?

Explanation opens after your attempt
Correct Answer

B. (x+3)

Explanation

Simple Explanation

मूल (r) होने पर गुणनखंड (x-r) होता है। (r=-3) के लिए गुणनखंड (x+3) होगा। / If the root is (r), the factor is (x-r). For (r=-3), the factor is (x+3).

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Question 42/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2+16=0\) के वास्तविक मूलों की संख्या कितनी है?

How many real roots does \(x^2+16=0\) have?

Explanation opens after your attempt
Correct Answer

C. (0)

Explanation

Simple Explanation

वास्तविक संख्या के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+16=0\) का कोई वास्तविक मूल नहीं है। / For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.

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Question 43/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-3x-10=0\) के मूल कौन से हैं?

What are the roots of \(x^2-3x-10=0\)?

Explanation opens after your attempt
Correct Answer

A. (5) और (-2)(5) and (-2)

Explanation

Simple Explanation

(x-2-3x-10=(x-5)(x+2)) है। इसलिए मूल (5) और (-2) हैं। / (x-2-3x-10=(x-5)(x+2)). Therefore the roots are (5) and (-2).

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Question 44/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2=49\) के मूल कौन से हैं?

What are the roots of \(x^2=49\)?

Explanation opens after your attempt
Correct Answer

A. (7) और (-7)(7) and (-7)

Explanation

Simple Explanation

\(x^2=49\) से \(x=\pm7\) मिलता है। वर्गमूल लेते समय दोनों चिन्ह लें। / From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.

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Question 45/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि एक मूल (5) है और मूलों का गुणनफल (35) है तो दूसरा मूल क्या होगा?

If one root is (5) and the product of roots is (35), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें। / The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

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Question 46/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि मूलों का योग (8) है और एक मूल (3) है तो दूसरा मूल क्या है?

If the sum of roots is (8) and one root is (3), what is the other root?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

दूसरा मूल (8-3=5) है। योग में से दिया हुआ मूल घटाएं। / The other root is (8-3=5). Subtract the given root from the sum.

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Question 47/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी द्विघात समीकरण के मूल (r) और (-r) हैं तो उनके योग का मान क्या होगा?

If the roots of a quadratic equation are (r) and (-r), what is their sum?

Explanation opens after your attempt
Correct Answer

C. (0)

Explanation

Simple Explanation

(r+(-r)=0) होता है। विपरीत मूलों का योग हमेशा (0) होता है। / (r+(-r)=0). The sum of opposite roots is always (0).

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Question 48/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(3x^2-10x+3=0\) के मूल कौन से हैं?

What are the roots of \(3x^2-10x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. (3) और \(\frac{1}{3}\)(3) and \(\frac{1}{3}\)

Explanation

Simple Explanation

(3x-2-10x+3=(3x-1)(x-3)) है। इसलिए मूल \(\frac{1}{3}\) और (3) हैं। / (3x-2-10x+3=(3x-1)(x-3)). Therefore the roots are \(\frac{1}{3}\) and (3).

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Question 49/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (-4) और (-4) हैं तो समीकरण कौन सा है?

If both roots of a monic quadratic equation are (-4) and (-4), which equation is it?

Explanation opens after your attempt
Correct Answer

A. \(x^2+8x+16=0\)

Explanation

Simple Explanation

दोनों मूल (-4) हों तो समीकरण ((x+4)2=0) होगा। इसे खोलने पर \(x^2+8x+16=0\) मिलता है। / If both roots are (-4), the equation is ((x+4)2=0). Expanding it gives \(x^2+8x+16=0\).

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Question 50/50 Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x=\frac{1}{2}\) समीकरण \(4x^2+px-3=0\) का मूल है तो (p) का मान क्या है?

If \(x=\frac{1}{2}\) is a root of \(4x^2+px-3=0\), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(x=\frac{1}{2}\) रखने पर \(1+\frac{p}{2}-3=0\) इसलिए (p=4)। भिन्न मूल रखते समय हर पद सावधानी से हल करें। / Putting \(x=\frac{1}{2}\) gives \(1+\frac{p}{2}-3=0\), so (p=4). When substituting a fractional root, solve each term carefully.

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