Class 10 quadratic equations MCQ Questions

Question 31/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2+5x+2=0\) के लिए सही प्रकृति चुनिए।

Choose the correct nature for \(2x^2+5x+2=0\).

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

(D=5²-4(2)(2)=9>0). Hence the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=5²-4(2)(2)=9>0). Hence the roots are real and distinct.

Step 3

Exam Tip

(D=5²-4(2)(2)=9>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 32/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?

If (D=0) and \(a\neq0\), how many distinct real roots will the quadratic equation have?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.

Step 2

Why this answer is correct

The correct answer is A. (1). At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.

Step 3

Exam Tip

(D=0) पर दोनों मूल समान होते हैं, इसलिए अलग-अलग वास्तविक मूलों की संख्या (1) है। ध्यान रखें मूल दो बार दोहरता है।

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Question 33/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=-7) हो तो मूलों की प्रकृति क्या होगी?

If (D=-7), what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(-7<0), so there will be no real roots. Never treat negative (D) as equal roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (-7<0), so there will be no real roots. Never treat negative (D) as equal roots.

Step 3

Exam Tip

(-7<0) है, इसलिए वास्तविक मूल नहीं होंगे। ऋणात्मक (D) को कभी समान मूल न मानें।

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Question 34/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=25) हो तो द्विघात समीकरण के मूलों के बारे में सही बात क्या है?

If (D=25), which statement about the roots of a quadratic equation is correct?

Explanation opens after your attempt

Correct Answer

A. मूल वास्तविक और असमान होंगेroots will be real and distinct

Step 1

Concept

(25>0), so the roots will be real and distinct. The sign of (D) is enough for nature.

Step 2

Why this answer is correct

The correct answer is A. मूल वास्तविक और असमान होंगे / roots will be real and distinct. (25>0), so the roots will be real and distinct. The sign of (D) is enough for nature.

Step 3

Exam Tip

(25>0) है, इसलिए मूल वास्तविक और असमान होंगे। (D) का केवल चिन्ह प्रकृति बताने के लिए काफी है।

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Question 35/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?

By observing \(4x^2-12x+9=0\), what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

\(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. \(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 3

Exam Tip

\(4x^2-12x+9\) एक पूर्ण वर्ग ((2x-3)²) है। इसलिए मूल समान वास्तविक हैं।

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Question 36/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के वास्तविक मूल नहीं होंगे?

Which equation will have no real roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2+3x+5=0\)

Step 1

Concept

For the first equation, (D=3²-4(1)(5)=-11<0). A negative discriminant gives no real roots.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x+5=0\). For the first equation, (D=3²-4(1)(5)=-11<0). A negative discriminant gives no real roots.

Step 3

Exam Tip

पहले समीकरण में (D=3²-4(1)(5)=-11<0) है। ऋणात्मक विविक्तकर वास्तविक मूल नहीं देता।

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Question 37/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के दो वास्तविक और समान मूल होंगे?

Which equation will have two real and equal roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2+10x+25=0\)

Step 1

Concept

In the first equation, (D=10²-4(1)(25)=0). A perfect square form often gives equal roots.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+10x+25=0\). In the first equation, (D=10²-4(1)(25)=0). A perfect square form often gives equal roots.

Step 3

Exam Tip

पहले समीकरण में (D=10²-4(1)(25)=0) है। पूर्ण वर्ग रूप अक्सर समान मूल देता है।

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Question 38/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के दो वास्तविक और असमान मूल होंगे?

Which equation will have two real and distinct roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2-7x+10=0\)

Step 1

Concept

For the first equation, (D=(-7)²-4(1)(10)=9>0). Hence its roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7x+10=0\). For the first equation, (D=(-7)²-4(1)(10)=9>0). Hence its roots are real and distinct.

Step 3

Exam Tip

पहले समीकरण में (D=(-7)²-4(1)(10)=9>0) है। इसलिए उसके मूल वास्तविक और असमान हैं।

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Question 39/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+kx+16=0\) के समान वास्तविक मूल होने के लिए (k) का कौन सा मान सही हो सकता है?

Which value of (k) can make \(x^2+kx+16=0\) have equal real roots?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.

Step 2

Why this answer is correct

The correct answer is A. (8). For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.

Step 3

Exam Tip

समान मूलों के लिए \(k^2-64=0\) होता है, इसलिए (k=8) या (k=-8)। दिए विकल्पों में (8) सही है।

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Question 40/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-8x+m=0\) में समान वास्तविक मूलों के लिए (m) क्या होगा?

In \(x^2-8x+m=0\), what is (m) for equal real roots?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

(D=(-8)²-4m=0) gives (m=16). Keep the discriminant zero for equal roots.

Step 2

Why this answer is correct

The correct answer is A. (16). (D=(-8)²-4m=0) gives (m=16). Keep the discriminant zero for equal roots.

Step 3

Exam Tip

(D=(-8)²-4m=0) से (m=16) मिलता है। बराबर मूलों के लिए विविक्तकर शून्य रखें।

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Question 41/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+6x+k=0\) के समान वास्तविक मूल होने के लिए (k) का मान क्या होगा?

For \(x^2+6x+k=0\) to have equal real roots, what should be the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.

Step 2

Why this answer is correct

The correct answer is A. (9). For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.

Step 3

Exam Tip

समान मूलों के लिए (D=0), इसलिए \(6^2-4k=0\) से (k=9)। ऐसे प्रश्न में (D=0) लगाएं।

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Question 42/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(5x^2+x+1=0\) के लिए मूलों की प्रकृति चुनिए।

Choose the nature of roots for \(5x^2+x+1=0\).

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=1²-4(5)(1)=-19<0). Therefore the equation has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=1²-4(5)(1)=-19<0). Therefore the equation has no real roots.

Step 3

Exam Tip

(D=1²-4(5)(1)=-19<0) है। इसलिए कोई वास्तविक मूल नहीं है।

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Question 43/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(3x^2+6x+3=0\) के मूल किस प्रकार के होंगे?

What type of roots will the equation \(3x^2+6x+3=0\) have?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

(D=6²-4(3)(3)=0). Hence both roots will be equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. (D=6²-4(3)(3)=0). Hence both roots will be equal and real.

Step 3

Exam Tip

(D=6²-4(3)(3)=0) है। इसलिए दोनों मूल समान वास्तविक होंगे।

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Question 44/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2-3x+1=0\) के लिए विविक्तकर का मान क्या है?

What is the value of the discriminant for \(2x^2-3x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The value is (D=(-3)²-4(2)(1)=1). A positive discriminant gives distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. (1). The value is (D=(-3)²-4(2)(1)=1). A positive discriminant gives distinct real roots.

Step 3

Exam Tip

(D=(-3)²-4(2)(1)=1) है। धनात्मक विविक्तकर असमान वास्तविक मूल देता है।

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Question 45/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+2x+5=0\) के मूलों के बारे में सही कथन क्या है?

Which statement is correct about the roots of \(x^2+2x+5=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

Here (D=2²-4(1)(5)=-16<0). So there are no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. Here (D=2²-4(1)(5)=-16<0). So there are no real roots.

Step 3

Exam Tip

यहां (D=2²-4(1)(5)=-16<0) है। इसलिए वास्तविक मूल नहीं हैं।

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Question 46/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-4x+4=0\) के मूलों की प्रकृति पहचानिए।

Identify the nature of roots of the equation \(x^2-4x+4=0\).

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

Here (D=(-4)²-4(1)(4)=0). (D=0) means equal real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. Here (D=(-4)²-4(1)(4)=0). (D=0) means equal real roots.

Step 3

Exam Tip

यहां (D=(-4)²-4(1)(4)=0) है। (D=0) समान वास्तविक मूल बताता है।

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Question 47/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-5x+6=0\) के मूलों की प्रकृति क्या है?

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

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

Here (D=(-5)²-4(1)(6)=1>0). So the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. Here (D=(-5)²-4(1)(6)=1>0). So the roots are real and distinct.

Step 3

Exam Tip

यहां (D=(-5)²-4(1)(6)=1>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 48/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि द्विघात समीकरण के लिए (D=0) हो तो मूल कैसे होंगे?

If (D=0) for a quadratic equation, how will the roots be?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

When (D=0), both roots are equal. These are also called repeated real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. When (D=0), both roots are equal. These are also called repeated real roots.

Step 3

Exam Tip

(D=0) होने पर दोनों मूल बराबर होते हैं। इसे दोहराए गए वास्तविक मूल भी कहते हैं।

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Question 49/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि द्विघात समीकरण के लिए (D>0) हो तो मूलों की प्रकृति क्या होगी?

If (D>0) for a quadratic equation, what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

When (D>0), two different real roots are obtained. Check the sign first in exams.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. When (D>0), two different real roots are obtained. Check the sign first in exams.

Step 3

Exam Tip

(D>0) होने पर दो अलग-अलग वास्तविक मूल मिलते हैं। चिन्ह देखकर प्रकृति तुरंत लिखें।

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Question 50/600 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

द्विघात समीकरण \(ax^2+bx+c=0\) के मूलों की प्रकृति जानने के लिए कौन सा व्यंजक प्रयोग होता है?

Which expression is used to determine the nature of roots of the quadratic equation \(ax^2+bx+c=0\)?

Explanation opens after your attempt

Correct Answer

A. \(b^2-4ac\)

Step 1

Concept

The discriminant is \(D=b^2-4ac\). In exams first identify (a,b,c) correctly.

Step 2

Why this answer is correct

The correct answer is A. \(b^2-4ac\). The discriminant is \(D=b^2-4ac\). In exams first identify (a,b,c) correctly.

Step 3

Exam Tip

विविक्तकर \(D=b^2-4ac\) होता है। परीक्षा में पहले (a,b,c) सही पहचानें।

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Question 51/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+px+q=0\) के मूल (p+2) और (q-2) हैं तथा (p+q=8) है, तो (p) का मान क्या होगा?

If roots of \(x^2+px+q=0\) are (p+2) and (q-2), and (p+q=8), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-8)

Step 1

Concept

The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).

Step 2

Why this answer is correct

The correct answer is A. (-8). The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).

Step 3

Exam Tip

मूलों का योग (-p) होता है और ((p+2)+(q-2)=p+q=8) है। इसलिए (-p=8), अतः (p=-8)।

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Question 52/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x^-2-(2k+5)x+\(k^2+5k+6\)=0) के मूल लगातार पूर्णांक हैं, तो वे मूल कौन-से होंगे?

If the roots of (x^-2-(2k+5)x+\(k^2+5k+6\)=0) are consecutive integers, what will those roots be?

Explanation opens after your attempt

Correct Answer

A. (k+2) और (k+3)(k+2) and (k+3)

Step 1

Concept

The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k^-2+5k+6) are correct.

Step 2

Why this answer is correct

The correct answer is A. (k+2) और (k+3) / (k+2) and (k+3). The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k^-2+5k+6) are correct.

Step 3

Exam Tip

मूलों का योग (2k+5) और गुणनफल \(k^2+5k+6\) है। ((k+2)+(k+3)=2k+5) और ((k+2)(k+3)=k^-2+5k+6) सही है।

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Question 53/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(3x^2-11x+6=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?

If \(\alpha,\beta\) are roots of \(3x^2-11x+6=0\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{85}{18} \)

Step 1

Concept

We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{11}{3}\) and \(\alpha\beta=2\), so the value is \(\frac{85}{18}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{85}{18} \). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{11}{3}\) and \(\alpha\beta=2\), so the value is \(\frac{85}{18}\).

Step 3

Exam Tip

\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=\frac{11}{3}\) और \(\alpha\beta=2\), इसलिए मान \(\frac{85}{18}\) है।

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Question 54/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+x-156=0\)

Step 1

Concept

After clearing denominators, (6{(x+3)²+(x-2)²}=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x-156=0\). After clearing denominators, (6{(x+3)²+(x-2)²}=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).

Step 3

Exam Tip

हर हटाने पर (6{(x+3)²+(x-2)²}=13(x+3)(x-2)) मिलता है। सरल करने पर \(x^2+x-156=0\) सही रूप है।

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Question 55/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-2ax+a^2-49=0\) है, तो मूलों का अंतर क्या होगा?

If \(x^2-2ax+a^2-49=0\), what will be the difference of the roots?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

The equation is ((x-a)²-49=0), so the roots are (a+7) and (a-7). Their difference is (14).

Step 2

Why this answer is correct

The correct answer is A. (14). The equation is ((x-a)²-49=0), so the roots are (a+7) and (a-7). Their difference is (14).

Step 3

Exam Tip

समीकरण ((x-a)²-49=0) है, इसलिए मूल (a+7) और (a-7) हैं। उनका अंतर (14) है।

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Question 56/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2+14x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?

The equation \(x^2+14x+k=0\) has no real roots. What is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. (k>49)

Step 1

Concept

For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).

Step 2

Why this answer is correct

The correct answer is A. (k>49). For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).

Step 3

Exam Tip

कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (196-4k<0), इसलिए (k>49)।

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Question 57/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-8x-33=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+5\alpha+5\beta\) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-8x-33=0\), what is \(\alpha\beta+5\alpha+5\beta\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).

Step 2

Why this answer is correct

The correct answer is A. (7). Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).

Step 3

Exam Tip

यहाँ \(\alpha+\beta=8\) और \(\alpha\beta=-33\) है। इसलिए (\alpha\beta+5\alpha+5\beta=-33+5(8)=7)।

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Question 58/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-19x+84=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-19x+84=0\), what is (\(\alpha+\beta\)²)?

Explanation opens after your attempt

Correct Answer

A. (361)

Step 1

Concept

The sum of roots is (19). Therefore (\(\alpha+\beta\)²=19²=361).

Step 2

Why this answer is correct

The correct answer is A. (361). The sum of roots is (19). Therefore (\(\alpha+\beta\)²=19²=361).

Step 3

Exam Tip

मूलों का योग (19) है। इसलिए (\(\alpha+\beta\)²=19²=361)।

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Question 59/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

एक समकोण त्रिभुज का आधार (x+5), ऊंचाई (x+9) और क्षेत्रफल (95) है। सही समीकरण कौन-सा है?

A right triangle has base (x+5), height (x+9), and area (95). Which equation is correct?

Explanation opens after your attempt

Correct Answer

A. \(x^2+14x-145=0\)

Step 1

Concept

The area is (\frac{1}{2}(x+5)(x+9)=95). Thus ((x+5)(x+9)=190) and \(x^2+14x-145=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+14x-145=0\). The area is (\frac{1}{2}(x+5)(x+9)=95). Thus ((x+5)(x+9)=190) and \(x^2+14x-145=0\).

Step 3

Exam Tip

क्षेत्रफल (\frac{1}{2}(x+5)(x+9)=95) होगा। इसलिए ((x+5)(x+9)=190) और \(x^2+14x-145=0\)।

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Question 60/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-20x+96=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-20x+96=0\), 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 (96-160+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 (96-160+64=0).

Step 3

Exam Tip

(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (96-160+64=0)।

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quadratic equations MCQ Questions for Class 10

Practice Questions

समीकरण \(2x^2+5x+2=0\) के लिए सही प्रकृति चुनिए।

Concept

Why this answer is correct

Exam Tip

यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?

Concept

Why this answer is correct

Exam Tip

यदि (D=-7) हो तो मूलों की प्रकृति क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि (D=25) हो तो द्विघात समीकरण के मूलों के बारे में सही बात क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?

Concept

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Exam Tip

किस समीकरण के वास्तविक मूल नहीं होंगे?

Concept

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Exam Tip

किस समीकरण के दो वास्तविक और समान मूल होंगे?

Concept

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Exam Tip

किस समीकरण के दो वास्तविक और असमान मूल होंगे?

Concept

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Exam Tip

समीकरण \(x^2+kx+16=0\) के समान वास्तविक मूल होने के लिए (k) का कौन सा मान सही हो सकता है?

Concept

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Exam Tip

समीकरण \(x^2-8x+m=0\) में समान वास्तविक मूलों के लिए (m) क्या होगा?

Concept

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Exam Tip

समीकरण \(x^2+6x+k=0\) के समान वास्तविक मूल होने के लिए (k) का मान क्या होगा?

Concept

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Exam Tip

समीकरण \(5x^2+x+1=0\) के लिए मूलों की प्रकृति चुनिए।

Concept

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Exam Tip

समीकरण \(3x^2+6x+3=0\) के मूल किस प्रकार के होंगे?

Concept

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Exam Tip

समीकरण \(2x^2-3x+1=0\) के लिए विविक्तकर का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+2x+5=0\) के मूलों के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-4x+4=0\) के मूलों की प्रकृति पहचानिए।

Concept

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Exam Tip

समीकरण \(x^2-5x+6=0\) के मूलों की प्रकृति क्या है?

Concept

Why this answer is correct

Exam Tip

यदि द्विघात समीकरण के लिए (D=0) हो तो मूल कैसे होंगे?

Concept

Why this answer is correct

Exam Tip

यदि द्विघात समीकरण के लिए (D>0) हो तो मूलों की प्रकृति क्या होगी?

Concept

Why this answer is correct

Exam Tip

द्विघात समीकरण \(ax^2+bx+c=0\) के मूलों की प्रकृति जानने के लिए कौन सा व्यंजक प्रयोग होता है?

Concept

यदि (x^-2-(2k+5)x+\(k^2+5k+6\)=0) के मूल लगातार पूर्णांक हैं, तो वे मूल कौन-से होंगे?

यदि \(x^2-19x+84=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?