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rational roots MCQ Questions for Class 10

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43 questions tagged with rational roots.

Question 31/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

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

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

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक परिमेय और असमान ((D=49))Two real rational and distinct ((D=49))

Step 1

Concept

Here (D=32-4(2)(-5)=49). It is a positive perfect square, so the roots are rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक परिमेय और असमान ((D=49)) / Two real rational and distinct ((D=49)). Here (D=32-4(2)(-5)=49). It is a positive perfect square, so the roots are rational and distinct.

Step 3

Exam Tip

यहाँ (D=32-4(2)(-5)=49) है। यह धनात्मक पूर्ण वर्ग है, इसलिए मूल परिमेय और असमान हैं।

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Question 32/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+7x+10=0\) में विविक्तकर और मूलों की प्रकृति क्या है?

What are the discriminant and nature of roots in \(x^2+7x+10=0\)?

Explanation opens after your attempt
Correct Answer

A. (D=9), दो वास्तविक परिमेय असमान(D=9), two real rational distinct

Step 1

Concept

Here (D=72-4(1)(10)=9). A positive perfect square gives rational distinct roots.

Step 2

Why this answer is correct

The correct answer is A. (D=9), दो वास्तविक परिमेय असमान / (D=9), two real rational distinct. Here (D=72-4(1)(10)=9). A positive perfect square gives rational distinct roots.

Step 3

Exam Tip

यहाँ (D=72-4(1)(10)=9) है। धनात्मक पूर्ण वर्ग से परिमेय असमान मूल मिलते हैं।

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Question 33/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(6x^2-x-2=0\) के लिए सही प्रकृति चुनिए।

Choose the correct nature for \(6x^2-x-2=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक परिमेय और असमान ((D=49))Two real rational and distinct ((D=49))

Step 1

Concept

Here (D=(-1)2-4(6)(-2)=49). A positive perfect-square (D) gives rational distinct roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक परिमेय और असमान ((D=49)) / Two real rational and distinct ((D=49)). Here (D=(-1)2-4(6)(-2)=49). A positive perfect-square (D) gives rational distinct roots.

Step 3

Exam Tip

यहाँ (D=(-1)2-4(6)(-2)=49) है। धनात्मक पूर्ण वर्ग (D) परिमेय असमान मूल देता है।

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Question 34/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2-7x+3=0\) के मूलों की प्रकृति पहचानिए।

Identify the nature of roots of \(2x^2-7x+3=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक परिमेय और असमान ((D=25))Two real rational and distinct ((D=25))

Step 1

Concept

Here (D=(-7)2-4(2)(3)=25). Since (25) is a perfect square, the roots are rational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक परिमेय और असमान ((D=25)) / Two real rational and distinct ((D=25)). Here (D=(-7)2-4(2)(3)=25). Since (25) is a perfect square, the roots are rational.

Step 3

Exam Tip

यहाँ (D=(-7)2-4(2)(3)=25) है। (25) पूर्ण वर्ग है, इसलिए मूल परिमेय हैं।

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Question 35/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि किसी द्विघात समीकरण का विविक्तकर (D=49) है, तो मूलों की प्रकृति क्या होगी?

If a quadratic equation has discriminant (D=49), what is the nature of its roots?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक परिमेय और असमानTwo real rational and distinct

Step 1

Concept

(D=49) is a positive perfect square. So the roots are real, rational, and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक परिमेय और असमान / Two real rational and distinct. (D=49) is a positive perfect square. So the roots are real, rational, and distinct.

Step 3

Exam Tip

(D=49) धनात्मक पूर्ण वर्ग है। इसलिए मूल वास्तविक, परिमेय और असमान होंगे।

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Question 36/43 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2-5x+2=0\) के मूलों के बारे में सही विकल्प चुनिए।

Choose the correct option about the roots of \(2x^2-5x+2=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक परिमेय और असमान ((D=9))Two real rational distinct ((D=9))

Step 1

Concept

Here (D=(-5)2-4(2)(2)=9). A positive perfect-square (D) gives rational distinct roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक परिमेय और असमान ((D=9)) / Two real rational distinct ((D=9)). Here (D=(-5)2-4(2)(2)=9). A positive perfect-square (D) gives rational distinct roots.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(2)(2)=9) है। धनात्मक पूर्ण वर्ग (D) परिमेय असमान मूल देता है।

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Question 37/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(6x^2-5x+1=0\) के लिए (D) क्या है?

What is (D) for \(6x^2-5x+1=0\)?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

Here (D=(-5)2-4(6)(1)=1). So the roots will be rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. (1). Here (D=(-5)2-4(6)(1)=1). So the roots will be rational and distinct.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(6)(1)=1) है। इसलिए मूल परिमेय और भिन्न होंगे।

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Question 38/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

कौन सा समीकरण वास्तविक, परिमेय और भिन्न मूल रखता है?

Which equation has real, rational and distinct roots?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

In the first equation (D=(-9)2-4(1)(20)=1). Hence the roots are real, rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-9x+20=0\). In the first equation (D=(-9)2-4(1)(20)=1). Hence the roots are real, rational and distinct.

Step 3

Exam Tip

पहले समीकरण में (D=(-9)2-4(1)(20)=1) है। इसलिए मूल वास्तविक, परिमेय और भिन्न हैं।

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Question 39/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि किसी द्विघात समीकरण में (D=25) है तो मूलों की प्रकृति क्या होगी?

If a quadratic equation has (D=25), what will be the nature of roots?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, परिमेय और भिन्नReal, rational and distinct

Step 1

Concept

(25>0) and (25) is a perfect square. Therefore the roots are real, rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, परिमेय और भिन्न / Real, rational and distinct. (25>0) and (25) is a perfect square. Therefore the roots are real, rational and distinct.

Step 3

Exam Tip

(25>0) है और (25) पूर्ण वर्ग है। इसलिए मूल वास्तविक, परिमेय और भिन्न होंगे।

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Question 40/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-6x+8=0\) के मूल कैसे होंगे?

How will the roots of \(x^2-6x+8=0\) be?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, परिमेय और भिन्नReal, rational and distinct

Step 1

Concept

Here (D=4>0) and (4) is a perfect square. So the roots are real, rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, परिमेय और भिन्न / Real, rational and distinct. Here (D=4>0) and (4) is a perfect square. So the roots are real, rational and distinct.

Step 3

Exam Tip

यहाँ (D=4>0) और (4) पूर्ण वर्ग है। इसलिए मूल वास्तविक, परिमेय और भिन्न हैं।

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Question 41/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-3x+2=0\) के मूलों की प्रकृति क्या है?

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

Explanation opens after your attempt
Correct Answer

A. वास्तविक, परिमेय और भिन्नReal, rational and distinct

Step 1

Concept

Here (D=1>0) and (1) is a perfect square. So the roots are real, rational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, परिमेय और भिन्न / Real, rational and distinct. Here (D=1>0) and (1) is a perfect square. So the roots are real, rational and distinct.

Step 3

Exam Tip

इसमें (D=1>0) है और (1) पूर्ण वर्ग है। इसलिए मूल वास्तविक, परिमेय और भिन्न हैं।

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Question 42/43 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (D>0) और (D) पूर्ण वर्ग हो तो मूलों की प्रकृति क्या होगी?

If (D>0) and (D) is a perfect square, what will be the nature of roots?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, परिमेय और भिन्नReal, rational and distinct

Step 1

Concept

A positive perfect square (D) gives real, rational and distinct roots. Check both the sign and perfect square condition of (D).

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, परिमेय और भिन्न / Real, rational and distinct. A positive perfect square (D) gives real, rational and distinct roots. Check both the sign and perfect square condition of (D).

Step 3

Exam Tip

धनात्मक पूर्ण वर्ग (D) से वास्तविक, परिमेय और भिन्न मूल मिलते हैं। (D) का चिन्ह और पूर्ण वर्ग दोनों देखें।

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Question 43/43 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

यदि \(x^2-4x+4=0\), तो मूलों की प्रकृति क्या है?

If \(x^2-4x+4=0\), what is the nature of the roots?

Explanation opens after your attempt
Correct Answer

B. दो समान परिमेयTwo equal rational roots

Step 1

Concept

The discriminant is (16-16=0), so the roots are equal and (x=2) is rational. In exams (D=0) means equal roots.

Step 2

Why this answer is correct

The correct answer is B. दो समान परिमेय / Two equal rational roots. The discriminant is (16-16=0), so the roots are equal and (x=2) is rational. In exams (D=0) means equal roots.

Step 3

Exam Tip

विविक्तकर (16-16=0), इसलिए मूल समान हैं और (x=2) परिमेय है। परीक्षा में (D=0) का अर्थ समान मूल होता है।

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