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always real roots MCQ Questions for Class 10

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2 questions tagged with always real roots.

Question 1/2 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (5x-2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

What is the correct condition for real roots of (5x-2-2(k+1)x+(k-3)=0)?

Explanation opens after your attempt
Correct Answer

A. \(k^2-3k+16\ge0\)

Step 1

Concept

Here (D=4[(k+1)2-5(k-3)]=4\(k^2-3k+16\)). This expression is always positive, so real roots always exist.

Step 2

Why this answer is correct

The correct answer is A. \(k^2-3k+16\ge0\). Here (D=4[(k+1)2-5(k-3)]=4\(k^2-3k+16\)). This expression is always positive, so real roots always exist.

Step 3

Exam Tip

यहाँ (D=4[(k+1)2-5(k-3)]=4\(k^2-3k+16\)) है। यह अभिव्यक्ति हमेशा धनात्मक है, इसलिए वास्तविक मूल हमेशा मिलेंगे।

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Question 2/2 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण (2x-2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?

Why are the roots of (2x-2-(3q+1)x+q=0) always real and distinct?

Explanation opens after your attempt
Correct Answer

A. क्योंकि \(D=9q^2-2q+1>0\)Because \(D=9q^2-2q+1>0\)

Step 1

Concept

Here (D=(3q+1)2-8q=9q-2-2q+1). Its own discriminant ((-2)2-4(9)(1)<0), so it is always positive.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(D=9q^2-2q+1>0\) / Because \(D=9q^2-2q+1>0\). Here (D=(3q+1)2-8q=9q-2-2q+1). Its own discriminant ((-2)2-4(9)(1)<0), so it is always positive.

Step 3

Exam Tip

यहाँ (D=(3q+1)2-8q=9q-2-2q+1) है। इसका अपना विविक्तकर ((-2)2-4(9)(1)<0) और मान सदैव धनात्मक है।

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