Concept-wise Practice

irrational roots MCQ Questions for Class 10

irrational roots se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

All Tags Search Similar

Practice Questions

70 questions tagged with irrational roots.

Question 1/70 Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

निम्न में से किस समीकरण के मूल वास्तविक, अपरिमेय और असमान हैं?

Which of the following equations has real, irrational, and distinct roots?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2\sqrt{2}x-1=0\)

Step 1

Concept

In option (A), (D=\(-2\sqrt{2}\)2-4(1)(-1)=12). (12) is positive but not a perfect square.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2\sqrt{2}x-1=0\). In option (A), (D=\(-2\sqrt{2}\)2-4(1)(-1)=12). (12) is positive but not a perfect square.

Step 3

Exam Tip

विकल्प (A) में (D=\(-2\sqrt{2}\)2-4(1)(-1)=12) है। (12) धनात्मक है पर पूर्ण वर्ग नहीं है।

Open Question Page
Ask Friends
Question 2/70 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (D=18) किसी द्विघात समीकरण का विविक्तकर है, तो मूलों के बारे में सही कथन क्या है?

If (D=18) is the discriminant of a quadratic equation, what is the correct statement about its roots?

Explanation opens after your attempt
Correct Answer

A. दो भिन्न वास्तविक और अपरिमेय मूलTwo distinct real and irrational roots

Step 1

Concept

(D=18) is positive but not a perfect square, so the roots are real, distinct, and irrational. In exams, also check whether (D) is a perfect square.

Step 2

Why this answer is correct

The correct answer is A. दो भिन्न वास्तविक और अपरिमेय मूल / Two distinct real and irrational roots. (D=18) is positive but not a perfect square, so the roots are real, distinct, and irrational. In exams, also check whether (D) is a perfect square.

Step 3

Exam Tip

(D=18) धनात्मक है लेकिन पूर्ण वर्ग नहीं है, इसलिए मूल वास्तविक भिन्न और अपरिमेय होंगे। परीक्षा में (D) के पूर्ण वर्ग होने की जांच भी करें।

Open Question Page
Ask Friends
Question 3/70 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

द्विघात समीकरण \(x^2-4x+1=0\) के मूलों की सही प्रकृति चुनिए।

Choose the correct nature of roots of \(x^2-4x+1=0\).

Explanation opens after your attempt
Correct Answer

A. दो भिन्न वास्तविक और अपरिमेय मूलTwo distinct real and irrational roots

Step 1

Concept

Here (D=(-4)2-4\cdot1\cdot1=12), which is positive but not a perfect square. In exams, such (D) gives irrational distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. दो भिन्न वास्तविक और अपरिमेय मूल / Two distinct real and irrational roots. Here (D=(-4)2-4\cdot1\cdot1=12), which is positive but not a perfect square. In exams, such (D) gives irrational distinct real roots.

Step 3

Exam Tip

यहां (D=(-4)2-4\cdot1\cdot1=12), जो धनात्मक है लेकिन पूर्ण वर्ग नहीं है। परीक्षा में ऐसा (D) अपरिमेय भिन्न वास्तविक मूल देता है।

Open Question Page
Ask Friends
Question 4/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(7x^2-5x-3=0\) के मूलों की प्रकृति क्या होगी?

What will be the nature of roots of \(7x^2-5x-3=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=109))Two real irrational and distinct ((D=109))

Step 1

Concept

Here (D=(-5)2-4(7)(-3)=109). (109) is positive but not a perfect square, so the roots are irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=109)) / Two real irrational and distinct ((D=109)). Here (D=(-5)2-4(7)(-3)=109). (109) is positive but not a perfect square, so the roots are irrational and distinct.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(7)(-3)=109) है। (109) धनात्मक है पर पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय और असमान हैं।

Open Question Page
Ask Friends
Question 5/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(4x^2-5x-2=0\) के मूलों की प्रकृति क्या होगी?

What will be the nature of roots of \(4x^2-5x-2=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=57))Two real irrational and distinct ((D=57))

Step 1

Concept

Here (D=(-5)2-4(4)(-2)=57). (57) is positive but not a perfect square, so the roots are irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=57)) / Two real irrational and distinct ((D=57)). Here (D=(-5)2-4(4)(-2)=57). (57) is positive but not a perfect square, so the roots are irrational and distinct.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(4)(-2)=57) है। (57) धनात्मक है पर पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय असमान हैं।

Open Question Page
Ask Friends
Question 6/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि \(D_1=64\), \(D_2=15\), \(D_3=0\) और \(D_4=-9\) हों, तो अपरिमेय असमान मूल किसमें होंगे?

If \(D_1=64\), \(D_2=15\), \(D_3=0\), and \(D_4=-9\), which one gives irrational distinct roots?

Explanation opens after your attempt
Correct Answer

A. \(D_2=15\)

Step 1

Concept

For irrational distinct roots, (D>0) and (D) must not be a perfect square. (15) satisfies this condition.

Step 2

Why this answer is correct

The correct answer is A. \(D_2=15\). For irrational distinct roots, (D>0) and (D) must not be a perfect square. (15) satisfies this condition.

Step 3

Exam Tip

अपरिमेय असमान मूलों के लिए (D>0) और (D) पूर्ण वर्ग नहीं होना चाहिए। (15) यह शर्त पूरी करता है।

Open Question Page
Ask Friends
Question 7/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(2x^2-7x+1=0\) के मूलों की प्रकृति बताइए।

State the nature of roots of \(2x^2-7x+1=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=41))Two real irrational and distinct ((D=41))

Step 1

Concept

Here (D=(-7)2-4(2)(1)=41). (41) is not a perfect square, so the roots are irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=41)) / Two real irrational and distinct ((D=41)). Here (D=(-7)2-4(2)(1)=41). (41) is not a perfect square, so the roots are irrational.

Step 3

Exam Tip

यहाँ (D=(-7)2-4(2)(1)=41) है। (41) पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय हैं।

Open Question Page
Ask Friends
Question 8/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि परवलय (x)-अक्ष को दो अलग बिंदुओं पर काटता है और (D) पूर्ण वर्ग नहीं है, तो मूल कैसे होंगे?

If a parabola cuts the (x)-axis at two different points and (D) is not a perfect square, how will the roots be?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमानTwo real irrational and distinct

Step 1

Concept

Two intersections mean (D>0). If (D) is not a perfect square, the roots are irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान / Two real irrational and distinct. Two intersections mean (D>0). If (D) is not a perfect square, the roots are irrational.

Step 3

Exam Tip

दो कटावों से (D>0) होता है। (D) पूर्ण वर्ग न हो तो मूल अपरिमेय होते हैं।

Open Question Page
Ask Friends
Question 9/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि किसी द्विघात समीकरण में (D=27) हो, तो मूलों की प्रकृति क्या होगी?

If a quadratic equation has (D=27), what will be the nature of roots?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमानTwo real irrational and distinct

Step 1

Concept

(D=27) is positive but not a perfect square. So the roots are real, distinct, and irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान / Two real irrational and distinct. (D=27) is positive but not a perfect square. So the roots are real, distinct, and irrational.

Step 3

Exam Tip

(D=27) धनात्मक है पर पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, असमान और अपरिमेय होंगे।

Open Question Page
Ask Friends
Question 10/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(3x^2-2x-2=0\) के मूल कैसे होंगे?

How will the roots of \(3x^2-2x-2=0\) be?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=28))Two real irrational and distinct ((D=28))

Step 1

Concept

Here (D=(-2)2-4(3)(-2)=28). (28) is not a perfect square, so the roots are irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=28)) / Two real irrational and distinct ((D=28)). Here (D=(-2)2-4(3)(-2)=28). (28) is not a perfect square, so the roots are irrational.

Step 3

Exam Tip

यहाँ (D=(-2)2-4(3)(-2)=28) है। (28) पूर्ण वर्ग नहीं है इसलिए मूल अपरिमेय हैं।

Open Question Page
Ask Friends
Question 11/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-x-1=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-x-1=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=5))Two real irrational and distinct ((D=5))

Step 1

Concept

Here (D=(-1)2-4(1)(-1)=5). (5) is positive but not a perfect square.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=5)) / Two real irrational and distinct ((D=5)). Here (D=(-1)2-4(1)(-1)=5). (5) is positive but not a perfect square.

Step 3

Exam Tip

यहाँ (D=(-1)2-4(1)(-1)=5) है। (5) धनात्मक है पर पूर्ण वर्ग नहीं है।

Open Question Page
Ask Friends
Question 12/70 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

एक विद्यार्थी ने (D=18) देखकर परिमेय मूल लिख दिए। सही सुधार क्या है?

A student sees (D=18) and writes rational roots. What is the correct correction?

Explanation opens after your attempt
Correct Answer

A. मूल वास्तविक, अपरिमेय और भिन्न होंगेThe roots will be real, irrational and distinct

Step 1

Concept

(18>0) but (18) is not a perfect square. Hence the roots are real, irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. मूल वास्तविक, अपरिमेय और भिन्न होंगे / The roots will be real, irrational and distinct. (18>0) but (18) is not a perfect square. Hence the roots are real, irrational and distinct.

Step 3

Exam Tip

(18>0) है पर (18) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न होंगे।

Open Question Page
Ask Friends
Question 13/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(3x^2-4x-1=0\) के मूलों की प्रकृति क्या होगी?

What will be the nature of roots of \(3x^2-4x-1=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=28))Two real irrational and distinct ((D=28))

Step 1

Concept

Here (D=(-4)2-4(3)(-1)=28). (28) is positive but not a perfect square, so the roots are irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=28)) / Two real irrational and distinct ((D=28)). Here (D=(-4)2-4(3)(-1)=28). (28) is positive but not a perfect square, so the roots are irrational and distinct.

Step 3

Exam Tip

यहाँ (D=(-4)2-4(3)(-1)=28) है। (28) धनात्मक है पर पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय असमान हैं।

Open Question Page
Ask Friends
Question 14/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि \(D_1=36\), \(D_2=11\), \(D_3=0\) और \(D_4=-5\) हों, तो अपरिमेय असमान मूल किसमें होंगे?

If \(D_1=36\), \(D_2=11\), \(D_3=0\), and \(D_4=-5\), which one gives irrational distinct roots?

Explanation opens after your attempt
Correct Answer

A. \(D_2=11\)

Step 1

Concept

For irrational distinct roots, (D>0) and (D) must not be a perfect square. (11) satisfies this condition.

Step 2

Why this answer is correct

The correct answer is A. \(D_2=11\). For irrational distinct roots, (D>0) and (D) must not be a perfect square. (11) satisfies this condition.

Step 3

Exam Tip

अपरिमेय असमान मूलों के लिए (D>0) और (D) पूर्ण वर्ग नहीं होना चाहिए। (11) इसी शर्त को पूरा करता है।

Open Question Page
Ask Friends
Question 15/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2-3x-1=0\) के मूलों की प्रकृति बताइए।

State the nature of roots of \(x^2-3x-1=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=13))Two real irrational and distinct ((D=13))

Step 1

Concept

Here (D=(-3)2-4(1)(-1)=13). Since (13) is not a perfect square, the roots are irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=13)) / Two real irrational and distinct ((D=13)). Here (D=(-3)2-4(1)(-1)=13). Since (13) is not a perfect square, the roots are irrational.

Step 3

Exam Tip

यहाँ (D=(-3)2-4(1)(-1)=13) है। (13) पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय हैं।

Open Question Page
Ask Friends
Question 16/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि किसी द्विघात समीकरण का (D=18) है, तो मूलों की प्रकृति क्या होगी?

If a quadratic equation has (D=18), what will be the nature of roots?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमानTwo real irrational and distinct

Step 1

Concept

(D=18) is positive but not a perfect square. So the roots are real, distinct, and irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान / Two real irrational and distinct. (D=18) is positive but not a perfect square. So the roots are real, distinct, and irrational.

Step 3

Exam Tip

(D=18) धनात्मक है पर पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, असमान और अपरिमेय होंगे।

Open Question Page
Ask Friends
Question 17/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2-7x+11=0\) के मूल कैसे होंगे?

How will the roots of \(x^2-7x+11=0\) be?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=5))Two real irrational and distinct ((D=5))

Step 1

Concept

Here (D=(-7)2-4(1)(11)=5). (D) is not a perfect square, so the roots are irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=5)) / Two real irrational and distinct ((D=5)). Here (D=(-7)2-4(1)(11)=5). (D) is not a perfect square, so the roots are irrational and distinct.

Step 3

Exam Tip

यहाँ (D=(-7)2-4(1)(11)=5) है। (D) पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय और असमान हैं।

Open Question Page
Ask Friends
Question 18/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2-5x+5=0\) के मूलों की प्रकृति पहचानिए।

Identify the nature of roots of \(x^2-5x+5=0\).

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=5))Two real irrational and distinct ((D=5))

Step 1

Concept

Here (D=(-5)2-4(1)(5)=5). (D) is positive but not a perfect square, so the roots are irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=5)) / Two real irrational and distinct ((D=5)). Here (D=(-5)2-4(1)(5)=5). (D) is positive but not a perfect square, so the roots are irrational.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(1)(5)=5) है। (D) धनात्मक है पर पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय हैं।

Open Question Page
Ask Friends
Question 19/70 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-2\sqrt{5}x+1=0\) के मूलों की प्रकृति चुनिए।

Choose the nature of roots of \(x^2-2\sqrt{5}x+1=0\).

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

Here (D=\(2\sqrt{5}\)2-4(1)(1)=16>0). The roots are \(\sqrt{5}\pm2\), so they are irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. Here (D=\(2\sqrt{5}\)2-4(1)(1)=16>0). The roots are \(\sqrt{5}\pm2\), so they are irrational and distinct.

Step 3

Exam Tip

यहाँ (D=\(2\sqrt{5}\)2-4(1)(1)=16>0) है। मूल \(\sqrt{5}\pm2\) होंगे, इसलिए वे अपरिमेय और भिन्न हैं।

Open Question Page
Ask Friends
Question 20/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-4x+1=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-4x+1=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमान ((D=12))Two real irrational and distinct ((D=12))

Step 1

Concept

Here (D=(-4)2-4(1)(1)=12). (12) is positive but not a perfect square.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=12)) / Two real irrational and distinct ((D=12)). Here (D=(-4)2-4(1)(1)=12). (12) is positive but not a perfect square.

Step 3

Exam Tip

यहाँ (D=(-4)2-4(1)(1)=12) है। (12) धनात्मक है पर पूर्ण वर्ग नहीं है।

Open Question Page
Ask Friends
Question 21/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि किसी समीकरण में (D=12) हो, तो मूलों की सही प्रकृति कौन सी होगी?

If an equation has (D=12), which is the correct nature of roots?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक अपरिमेय और असमानTwo real irrational and distinct

Step 1

Concept

(D=12) is positive but not a perfect square. So roots are real distinct and irrational.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक अपरिमेय और असमान / Two real irrational and distinct. (D=12) is positive but not a perfect square. So roots are real distinct and irrational.

Step 3

Exam Tip

(D=12) धनात्मक है पर पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक असमान और अपरिमेय होते हैं।

Open Question Page
Ask Friends
Question 22/70 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-3x+1=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-3x+1=0\)?

Explanation opens after your attempt
Correct Answer

A. वास्तविक असमान और अपरिमेय ((D=5))Real distinct and irrational ((D=5))

Step 1

Concept

Here (D=9-4=5), which is positive but not a perfect square. So roots are real distinct and irrational.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक असमान और अपरिमेय ((D=5)) / Real distinct and irrational ((D=5)). Here (D=9-4=5), which is positive but not a perfect square. So roots are real distinct and irrational.

Step 3

Exam Tip

यहाँ (D=9-4=5) है जो धनात्मक है पर पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक असमान और अपरिमेय हैं।

Open Question Page
Ask Friends
Question 23/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

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

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

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

Here (D=(-5)2-4(1)(3)=13), and (13) is not a perfect square. So the roots are real, irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. Here (D=(-5)2-4(1)(3)=13), and (13) is not a perfect square. So the roots are real, irrational and distinct.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(1)(3)=13) है और (13) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न हैं।

Open Question Page
Ask Friends
Question 24/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(3x^2-6x+1=0\) में (D) का मान क्या है?

What is the value of (D) in \(3x^2-6x+1=0\)?

Explanation opens after your attempt
Correct Answer

A. (24)

Step 1

Concept

Here (D=(-6)2-4(3)(1)=24). (24) is positive but not a perfect square.

Step 2

Why this answer is correct

The correct answer is A. (24). Here (D=(-6)2-4(3)(1)=24). (24) is positive but not a perfect square.

Step 3

Exam Tip

यहाँ (D=(-6)2-4(3)(1)=24) है। (24) धनात्मक है लेकिन पूर्ण वर्ग नहीं है।

Open Question Page
Ask Friends
Question 25/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

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

Which equation has real, irrational and distinct roots?

Explanation opens after your attempt
Correct Answer

B. \(x^2-2x-2=0\)

Step 1

Concept

In the second equation (D=(-2)2-4(1)(-2)=12). (12) is positive but not a perfect square.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-2x-2=0\). In the second equation (D=(-2)2-4(1)(-2)=12). (12) is positive but not a perfect square.

Step 3

Exam Tip

दूसरे समीकरण में (D=(-2)2-4(1)(-2)=12) है। (12) धनात्मक है पर पूर्ण वर्ग नहीं है।

Open Question Page
Ask Friends
Question 26/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि किसी द्विघात समीकरण में (D=5) है तो सही निष्कर्ष क्या है?

If a quadratic equation has (D=5), what is the correct conclusion?

Explanation opens after your attempt
Correct Answer

A. मूल वास्तविक, अपरिमेय और भिन्न हैंRoots are real, irrational and distinct

Step 1

Concept

(5>0), but (5) is not a perfect square. So the roots are real, irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. मूल वास्तविक, अपरिमेय और भिन्न हैं / Roots are real, irrational and distinct. (5>0), but (5) is not a perfect square. So the roots are real, irrational and distinct.

Step 3

Exam Tip

(5>0) है लेकिन (5) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न होंगे।

Open Question Page
Ask Friends
Question 27/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-2x-1=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-2x-1=0\)?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

(D=8>0), but (8) is not a perfect square. Hence the roots are real, irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. (D=8>0), but (8) is not a perfect square. Hence the roots are real, irrational and distinct.

Step 3

Exam Tip

(D=8>0) है लेकिन (8) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न हैं।

Open Question Page
Ask Friends
Question 28/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-4x+1=0\) के मूल कैसे होंगे?

How will the roots of \(x^2-4x+1=0\) be?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

Here (D=12>0) and (12) is not a perfect square. Therefore the roots are real, irrational and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. Here (D=12>0) and (12) is not a perfect square. Therefore the roots are real, irrational and distinct.

Step 3

Exam Tip

इसमें (D=12>0) है और (12) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न होंगे।

Open Question Page
Ask Friends
Question 29/70 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (D>0) और (D) पूर्ण वर्ग नहीं है तो मूल कैसे होंगे?

If (D>0) and (D) is not a perfect square, how will the roots be?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

A positive non-perfect-square (D) gives real, irrational and distinct roots. Only (D>0) tells distinctness.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. A positive non-perfect-square (D) gives real, irrational and distinct roots. Only (D>0) tells distinctness.

Step 3

Exam Tip

धनात्मक लेकिन अपूर्ण वर्ग (D) से मूल वास्तविक, अपरिमेय और भिन्न होते हैं। केवल (D>0) से भिन्नता पता चलती है।

Open Question Page
Ask Friends
Question 30/70 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2+14x+10=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?

If \(x^2+14x+10=0\), which form is correct by completing square?

Explanation opens after your attempt
Correct Answer

A. ((x+7)2=39)

Step 1

Concept

Adding (49) to \(x^2+14x=-10\) gives ((x+7)2=39). In exams, add the same number to both sides.

Step 2

Why this answer is correct

The correct answer is A. ((x+7)2=39). Adding (49) to \(x^2+14x=-10\) gives ((x+7)2=39). In exams, add the same number to both sides.

Step 3

Exam Tip

\(x^2+14x=-10\) में (49) जोड़ने पर ((x+7)2=39) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।

Open Question Page
Ask Friends

irrational roots Revision Links

All MCQ Tags

Browse concept directory

All Subjects

Subject-wise practice

Search irrational roots

More keyword results