Class 10 quadratic equations MCQ Questions

Question 61/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+px+q=0\) के मूल (6) और (p) हैं, तो (p) का मान क्या होगा?

If the roots of \(x^2+px+q=0\) are (6) and (p), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).

Step 2

Why this answer is correct

The correct answer is A. (-3). The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).

Step 3

Exam Tip

मूलों का योग (6+p) है और समीकरण में योग (-p) होता है। इसलिए (6+p=-p), जिससे (p=-3) मिलता है।

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Question 62/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-9x+4=0\) के मूल \(\alpha,\beta\) हैं। \(\alpha+\beta+5\alpha\beta\) का मान क्या है?

The roots of \(x^2-9x+4=0\) are \(\alpha,\beta\). What is \(\alpha+\beta+5\alpha\beta\)?

Explanation opens after your attempt

Correct Answer

A. (29)

Step 1

Concept

The sum of roots is (9) and the product is (4). Therefore \(\alpha+\beta+5\alpha\beta=9+20=29\).

Step 2

Why this answer is correct

The correct answer is A. (29). The sum of roots is (9) and the product is (4). Therefore \(\alpha+\beta+5\alpha\beta=9+20=29\).

Step 3

Exam Tip

मूलों का योग (9) और गुणनफल (4) है। इसलिए \(\alpha+\beta+5\alpha\beta=9+20=29\)।

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Question 63/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x^-2+(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?

If (x=-1) is a root of (x^-2+(6k-3)x+5k=0), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).

Step 2

Why this answer is correct

The correct answer is A. (2). Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).

Step 3

Exam Tip

(x=-1) रखने पर (1-(6k-3)+5k=0) मिलता है। इससे (4-k=0), इसलिए (k=4) होगा।

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Question 64/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण ((x+6)²+(x-7)²=(x+3)²) का मानक रूप कौन-सा है?

What is the standard form of ((x+6)²+(x-7)²=(x+3)²)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-14x+76=0\)

Step 1

Concept

Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-14x+76=0\). Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-2x+85\) और दाईं ओर \(x^2+6x+9\) है। घटाने पर \(x^2-8x+76=0\) नहीं बल्कि \(x^2-8x+76=0\) मिलता है।

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Question 65/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (a=-4) हो, तो ((a+4)x^-2+\(a^2-16\)x+13=0) किस प्रकार का कथन बनेगा?

If (a=-4), what type of statement will ((a+4)x^-2+\(a^2-16\)x+13=0) become?

Explanation opens after your attempt

Correct Answer

A. विरोधाभासी कथनContradictory statement

Step 1

Concept

Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.

Step 2

Why this answer is correct

The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.

Step 3

Exam Tip

(a=-4) रखने पर \(0x^2+0x+13=0\) मिलता है। यह (13=0) है, जो विरोधाभासी कथन है।

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Question 66/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+bx+c=0\) के मूल (-6) और (13) हैं, तो (b+c) का मान क्या है?

If the roots of \(x^2+bx+c=0\) are (-6) and (13), what is the value of (b+c)?

Explanation opens after your attempt

Correct Answer

A. (-85)

Step 1

Concept

The sum of roots is (7), so (b=-7), and the product is (-78), so (c=-78). Therefore (b+c=-85).

Step 2

Why this answer is correct

The correct answer is A. (-85). The sum of roots is (7), so (b=-7), and the product is (-78), so (c=-78). Therefore (b+c=-85).

Step 3

Exam Tip

मूलों का योग (7) है, इसलिए (b=-7), और गुणनफल (-78) है, इसलिए (c=-78)। अतः (b+c=-85)।

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Question 67/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-7x-18=0\)?

Explanation opens after your attempt

Correct Answer

A. (721)

Step 1

Concept

The sum of roots is (7) and the product is (-18). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 2

Why this answer is correct

The correct answer is A. (721). The sum of roots is (7) and the product is (-18). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 3

Exam Tip

मूलों का योग (7) और गुणनफल (-18) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721)।

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Question 68/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(6x^2+kx+66=0\) में मूलों का गुणनफल मूलों के योग का (-2) गुना है, तो (k) क्या होगा?

If in \(6x^2+kx+66=0\), the product of roots is (-2) times the sum of roots, what is (k)?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).

Step 2

Why this answer is correct

The correct answer is A. (33). The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).

Step 3

Exam Tip

गुणनफल (11) और योग \(-\frac{k}{6}\) है। (11=-2\left\(-\frac{k}{6}\right\)) से (k=33) मिलता है।

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Question 69/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?

Which quadratic equation has sum of roots (0) and product (-169)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-169=0\)

Step 1

Concept

\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2-169=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-169) रखने पर (x^2-169=0) मिलता है\)।

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Question 70/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x=3) समीकरण \(kx^2-8x+5=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?

If (x=3) is not a root of \(kx^2-8x+5=0\), what condition must (k) satisfy?

Explanation opens after your attempt

Correct Answer

A. \(k\neq \frac{19}{9}\)

Step 1

Concept

Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).

Step 2

Why this answer is correct

The correct answer is A. \(k\neq \frac{19}{9}\). Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).

Step 3

Exam Tip

(x=3) रखने पर बायां पक्ष (9k-24+5=9k-19) होता है। मूल न होने के लिए \(9k-19\neq0\), इसलिए \(k\neq\frac{19}{9}\)।

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Question 71/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2+px+49=0\) के मूल समान और ऋणात्मक हैं। (p) का मान क्या होगा?

The roots of \(x^2+px+49=0\) are equal and negative. What is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).

Step 2

Why this answer is correct

The correct answer is A. (14). For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).

Step 3

Exam Tip

समान मूलों के लिए \(p^2-196=0\) से \(p=\pm14\) मिलता है। ऋणात्मक समान मूल के लिए \(-\frac{p}{2}<0\), इसलिए (p=14)।

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Question 72/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+mx+64=0\) का एक मूल दूसरे का व्युत्क्रम है, तो (m) के बारे में क्या कहा जा सकता है?

If one root of \(x^2+mx+64=0\) is the reciprocal of the other, what can be said about (m)?

Explanation opens after your attempt

Correct Answer

A. ऐसा संभव नहीं हैIt is not possible

Step 1

Concept

If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (64), 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. If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (64), so it is not possible.

Step 3

Exam Tip

एक मूल दूसरे का व्युत्क्रम हो तो मूलों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (64) है, इसलिए ऐसा संभव नहीं है।

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Question 73/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(36x^2-60kx+25k^2=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(36x^2-60kx+25k^2=0\)?

Explanation opens after your attempt

Correct Answer

A. दो समान वास्तविक मूलTwo equal real roots

Step 1

Concept

It can be written as ((6x-5k)²=0). Therefore both roots are equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो समान वास्तविक मूल / Two equal real roots. It can be written as ((6x-5k)²=0). Therefore both roots are equal and real.

Step 3

Exam Tip

यह ((6x-5k)²=0) के रूप में लिखा जा सकता है। इसलिए दोनों मूल समान वास्तविक होते हैं।

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Question 74/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि ((x+a)²=x^-2+28x+196) है, तो (a) का मान क्या होगा?

If ((x+a)²=x^-2+28x+196), what is the value of (a)?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

((x+a)²=x^-2+2ax+a^-2). From (2a=28), we get (a=14).

Step 2

Why this answer is correct

The correct answer is A. (14). ((x+a)²=x^-2+2ax+a^-2). From (2a=28), we get (a=14).

Step 3

Exam Tip

((x+a)²=x^-2+2ax+a^-2) होता है। (2a=28) से (a=14) मिलता है।

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Question 75/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-17x+72=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?

If \(\alpha,\beta\) are roots of \(x^2-17x+72=0\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{17}{72} \)

Step 1

Concept

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{17}{72}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{17}{72} \). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{17}{72}\).

Step 3

Exam Tip

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ मान \(\frac{17}{72}\) है।

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Question 76/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

दो संख्याओं का योग (19) और गुणनफल (90) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?

Two numbers have sum (19) and product (90). They can be roots of which quadratic equation?

Explanation opens after your attempt

Correct Answer

A. \(x^2-19x+90=0\)

Step 1

Concept

If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-19x+90=0\). If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.

Step 3

Exam Tip

यदि मूलों का योग (19) और गुणनफल (90) है, तो समीकरण \(x^2-19x+90=0\) होगा। मोनिक रूप का सूत्र याद रखें।

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Question 77/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

एक आयत की लंबाई (x+10) और चौड़ाई (x-7) है। क्षेत्रफल (160) हो तो सही समीकरण कौन-सा है?

A rectangle has length (x+10) and breadth (x-7). If its area is (160), which equation is correct?

Explanation opens after your attempt

Correct Answer

A. \(x^2+3x-230=0\)

Step 1

Concept

The area is ((x+10)(x-7)=160). Expanding gives \(x^2+3x-70=160\), so \(x^2+3x-230=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x-230=0\). The area is ((x+10)(x-7)=160). Expanding gives \(x^2+3x-70=160\), so \(x^2+3x-230=0\).

Step 3

Exam Tip

क्षेत्रफल ((x+10)(x-7)=160) होगा। विस्तार से \(x^2+3x-70=160\), इसलिए \(x^2+3x-230=0\)।

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Question 78/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?

In which option will the sum of roots be positive and the product of roots be positive?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-9x+20=0\). In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.

Step 3

Exam Tip

पहले विकल्प में योग \(-\frac{b}{a}=9\) और गुणनफल \(\frac{c}{a}=20\) है। इसलिए दोनों धनात्मक हैं।

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Question 79/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि समीकरण \(x^2+bx+144=0\) के दोनों मूल समान हैं और उनका मान (-12) है, तो (b) क्या है?

If both roots of \(x^2+bx+144=0\) are equal and their value is (-12), what is (b)?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).

Step 2

Why this answer is correct

The correct answer is A. (24). Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).

Step 3

Exam Tip

दोनों मूल (-12) हैं, इसलिए योग (-24) है। यहाँ मूलों का योग (-b) है, अतः (b=24)।

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Question 80/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+24x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?

If \(x^2+24x+c=0\) is a perfect square quadratic equation, what is the value of (c)?

Explanation opens after your attempt

Correct Answer

A. (144)

Step 1

Concept

For a perfect square, (x^-2+24x+c=(x+12)²) is needed. Hence (c=144).

Step 2

Why this answer is correct

The correct answer is A. (144). For a perfect square, (x^-2+24x+c=(x+12)²) is needed. Hence (c=144).

Step 3

Exam Tip

पूर्ण वर्ग के लिए (x^-2+24x+c=(x+12)²) होना चाहिए। इसलिए (c=144) होगा।

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Question 81/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(7x^2-30x+32=0\) में मूलों का अंतर क्या है?

What is the difference between the roots of \(7x^2-30x+32=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{2}{7} \)

Step 1

Concept

The roots are (2) and \(\frac{16}{7}\). Their difference is \(\frac{16}{7}-2=\frac{2}{7}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{2}{7} \). The roots are (2) and \(\frac{16}{7}\). Their difference is \(\frac{16}{7}-2=\frac{2}{7}\).

Step 3

Exam Tip

मूल (2) और \(\frac{16}{7}\) हैं। उनका अंतर \(\frac{16}{7}-2=\frac{2}{7}\) है।

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Question 82/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x^-2-(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+7)x+7m=0) is (7), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).

Step 3

Exam Tip

मूलों का गुणनफल (7m) है और एक मूल (7) है। इसलिए दूसरा मूल \(\frac{7m}{7}=m\) है।

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Question 83/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-12x+40=0\) के लिए कौन-सा कथन सही है?

Which statement is correct for \(x^2-12x+40=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहीं हैंIt has no real roots

Step 1

Concept

Here (D=(-12)²-4\cdot1\cdot40=-16<0). Therefore it has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं हैं / It has no real roots. Here (D=(-12)²-4\cdot1\cdot40=-16<0). Therefore it has no real roots.

Step 3

Exam Tip

यहाँ (D=(-12)²-4\cdot1\cdot40=-16<0) है। इसलिए वास्तविक मूल नहीं होंगे।

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Question 84/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि किसी मोनिक द्विघात समीकरण के मूल (3r) और (4r) हैं तथा उनका योग (28) है, तो उस समीकरण का स्थिर पद क्या होगा?

If the roots of a monic quadratic equation are (3r) and (4r), and their sum is (28), what will be the constant term?

Explanation opens after your attempt

Correct Answer

A. (192)

Step 1

Concept

From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).

Step 2

Why this answer is correct

The correct answer is A. (192). From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).

Step 3

Exam Tip

(3r+4r=28) से (r=4) मिलता है, इसलिए मूल (12) और (16) हैं। स्थिर पद मूलों का गुणनफल (192) होगा।

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Question 85/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण ((x+5)(x+8)+(x-4)(x+7)=110) का मानक रूप कौन-सा है?

What is the standard form of ((x+5)(x+8)+(x-4)(x+7)=110)?

Explanation opens after your attempt

Correct Answer

A. \(2x^2+16x-98=0\)

Step 1

Concept

The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+16x-98=0\). The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\) है। (110) घटाने पर \(2x^2+16x-98=0\) मिलता है।

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Question 86/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-18x+80=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-18x+80=0\), what is (\(\alpha-8\)\(\beta-8\))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).

Step 2

Why this answer is correct

The correct answer is A. (0). (\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).

Step 3

Exam Tip

(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (80-144+64=0)।

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Question 87/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(6x^2+7x+2=0\) में मूलों के वर्गों का योग क्या है?

What is the sum of squares of the roots of \(6x^2+7x+2=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{25}{36} \)

Step 1

Concept

(\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta). Here (\left\(-\frac{7}{6}\right\)²-2\cdot\frac{1}{3}=\frac{25}{36}).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{25}{36} \). (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta). Here (\left\(-\frac{7}{6}\right\)²-2\cdot\frac{1}{3}=\frac{25}{36}).

Step 3

Exam Tip

(\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) होता है। यहाँ (\left\(-\frac{7}{6}\right\)²-2\cdot\frac{1}{3}=\frac{25}{36})।

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Question 88/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+ax+54=0\) का एक मूल (6) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+54=0\) is (6), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (9), (a=-15)other root (9), (a=-15)

Step 1

Concept

The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15). The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).

Step 3

Exam Tip

मूलों का गुणनफल (54) है, इसलिए दूसरा मूल (9) होगा। योग (15) है और (-a=15), इसलिए (a=-15)।

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Question 89/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस समीकरण का विवेचक (-47) है?

Which equation has discriminant (-47)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+x+12=0\)

Step 1

Concept

For \(x^2+x+12=0\), \(D=1^2-4\cdot1\cdot12=-47\). Subtract the full (4ac) in the discriminant.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x+12=0\). For \(x^2+x+12=0\), \(D=1^2-4\cdot1\cdot12=-47\). Subtract the full (4ac) in the discriminant.

Step 3

Exam Tip

\(x^2+x+12=0\) के लिए \(D=1^2-4\cdot1\cdot12=-47\) है। विवेचक में (4ac) पूरा घटाएं।

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Question 90/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-20x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?

If the roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. (k<100)

Step 1

Concept

For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).

Step 2

Why this answer is correct

The correct answer is A. (k<100). For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).

Step 3

Exam Tip

भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (400-4k>0), इसलिए (k<100)।

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quadratic equations MCQ Questions for Class 10

Practice Questions

यदि \(x^2+px+q=0\) के मूल (6) और (p) हैं, तो (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-9x+4=0\) के मूल \(\alpha,\beta\) हैं। \(\alpha+\beta+5\alpha\beta\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (x-2+(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण ((x+6)2+(x-7)2=(x+3)2) का मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (a=-4) हो, तो ((a+4)x-2+\(a^2-16\)x+13=0) किस प्रकार का कथन बनेगा?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+bx+c=0\) के मूल (-6) और (13) हैं, तो (b+c) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(6x^2+kx+66=0\) में मूलों का गुणनफल मूलों के योग का (-2) गुना है, तो (k) क्या होगा?

Concept

Why this answer is correct

Exam Tip

किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?

Concept

Why this answer is correct

Exam Tip

यदि (x=3) समीकरण \(kx^2-8x+5=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+px+49=0\) के मूल समान और ऋणात्मक हैं। (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+mx+64=0\) का एक मूल दूसरे का व्युत्क्रम है, तो (m) के बारे में क्या कहा जा सकता है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(36x^2-60kx+25k^2=0\) के मूलों की प्रकृति क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ((x+a)2=x-2+28x+196) है, तो (a) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-17x+72=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?

Concept

Why this answer is correct

Exam Tip

दो संख्याओं का योग (19) और गुणनफल (90) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?

Concept

Why this answer is correct

Exam Tip

एक आयत की लंबाई (x+10) और चौड़ाई (x-7) है। क्षेत्रफल (160) हो तो सही समीकरण कौन-सा है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?

Concept

Why this answer is correct

Exam Tip

यदि समीकरण \(x^2+bx+144=0\) के दोनों मूल समान हैं और उनका मान (-12) है, तो (b) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+24x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?

Concept

यदि (x^-2+(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?

समीकरण ((x+6)²+(x-7)²=(x+3)²) का मानक रूप कौन-सा है?

यदि (a=-4) हो, तो ((a+4)x^-2+\(a^2-16\)x+13=0) किस प्रकार का कथन बनेगा?

यदि ((x+a)²=x^-2+28x+196) है, तो (a) का मान क्या होगा?

यदि (x^-2-(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?