Class 10 quadratic inequality MCQ Questions

Question 1/1 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (3x^-2-2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूलों के लिए (a) पर क्या शर्त है?

What condition on (a) is needed for real roots of (3x^-2-2(2a+1)x+\(a^2+a+1\)=0)?

Explanation opens after your attempt

Correct Answer

A. \(a^2+a-2\ge0\)

Step 1

Concept

Here (D=4(2a+1)²-12\(a^2+a+1\)=4\(a^2+a-2\)). For real roots, it must be (0) or more.

Step 2

Why this answer is correct

The correct answer is A. \(a^2+a-2\ge0\). Here (D=4(2a+1)²-12\(a^2+a+1\)=4\(a^2+a-2\)). For real roots, it must be (0) or more.

Step 3

Exam Tip

यहाँ (D=4(2a+1)²-12\(a^2+a+1\)=4\(a^2+a-2\)) है। वास्तविक मूलों के लिए यह (0) या अधिक होना चाहिए।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Hard
Level: 38

Question Hindi:
समीकरण (3x^2-2(2a+1)x+(a^2+a+1)=0) के वास्तविक मूलों के लिए (a) पर क्या शर्त है?

Question English:
What condition on (a) is needed for real roots of (3x^2-2(2a+1)x+(a^2+a+1)=0)?

Options:
A. (a^2+a-2\ge0)
B. (a^2+a-2<0)
C. (a^2+a+2\ge0)
D. (a=0) केवल / (a=0) only

Correct Answer:
A. (a^2+a-2\ge0)

Explanation Hindi:
यहाँ (D=4(2a+1)^2-12(a^2+a+1)=4(a^2+a-2)) है। वास्तविक मूलों के लिए यह (0) या अधिक होना चाहिए।

Explanation English:
Here (D=4(2a+1)^2-12(a^2+a+1)=4(a^2+a-2)). For real roots, it must be (0) or more.

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quadratic inequality MCQ Questions for Class 10

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समीकरण (3x^-2-2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूलों के लिए (a) पर क्या शर्त है?

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quadratic inequality MCQ Questions for Class 10

Practice Questions

समीकरण (3x-2-2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूलों के लिए (a) पर क्या शर्त है?

Concept

Why this answer is correct

Exam Tip

quadratic inequality Revision Links

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Search quadratic inequality

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समीकरण (3x^-2-2(2a+1)x+\(a^2+a+1\)=0) के वास्तविक मूलों के लिए (a) पर क्या शर्त है?