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discriminant-condition MCQ Questions for Class 10

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4 questions tagged with discriminant-condition.

Question 1/4 Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

(9x-2-6(a+1)x+a-2-3a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?

For (9x-2-6(a+1)x+a-2-3a=0) to have real roots, what is the correct condition on (a)?

Explanation opens after your attempt
Correct Answer

A. \(a\ge-\frac{1}{5}\)

Step 1

Concept

For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).

Step 2

Why this answer is correct

The correct answer is A. \(a\ge-\frac{1}{5}\). For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).

Step 3

Exam Tip

वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=36(5a+1)), इसलिए \(a\ge-\frac{1}{5}\)।

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Question 2/4 Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

(4x-2-4(a-1)x+a-2-4a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?

For (4x-2-4(a-1)x+a-2-4a=0) to have real roots, what is the correct condition on (a)?

Explanation opens after your attempt
Correct Answer

A. \(a\le1\)

Step 1

Concept

For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).

Step 2

Why this answer is correct

The correct answer is A. \(a\le1\). For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).

Step 3

Exam Tip

वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=16(1-a)), इसलिए \(a\le1\) है।

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Question 3/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

किस शर्त में \(x^2+bx+c\) के शून्यक परिमेय नहीं बल्कि वास्तविक होंगे?

Under which condition will the zeroes of \(x^2+bx+c\) be real but not rational?

Explanation opens after your attempt
Correct Answer

A. \(b^2-4c\) धनात्मक अपूर्ण वर्ग हो\(b^2-4c\) is positive and not a perfect square

Step 1

Concept

For real zeroes, the discriminant must be positive, and for irrational zeroes it must not be a perfect square. This is the key check for quadratics with rational coefficients.

Step 2

Why this answer is correct

The correct answer is A. \(b^2-4c\) धनात्मक अपूर्ण वर्ग हो / \(b^2-4c\) is positive and not a perfect square. For real zeroes, the discriminant must be positive, and for irrational zeroes it must not be a perfect square. This is the key check for quadratics with rational coefficients.

Step 3

Exam Tip

वास्तविक शून्यकों के लिए विविक्तकर धनात्मक चाहिए और अपरिमेय शून्यकों के लिए वह पूर्ण वर्ग नहीं होना चाहिए। परिमेय गुणांकों वाले द्विघात में यही मुख्य जाँच है।

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Question 4/4 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

किस स्थिति में \(x^2-5x+c\) के शून्यक वास्तविक और अपरिमेय होंगे?

In which case will the zeroes of \(x^2-5x+c\) be real and irrational?

Explanation opens after your attempt
Correct Answer

B. जब (25-4c) धनात्मक हो पर पूर्ण वर्ग न होWhen (25-4c) is positive but not a perfect square

Step 1

Concept

For real distinct zeroes, (D>0) is required. For irrational zeroes, (D) must not be a perfect square.

Step 2

Why this answer is correct

The correct answer is B. जब (25-4c) धनात्मक हो पर पूर्ण वर्ग न हो / When (25-4c) is positive but not a perfect square. For real distinct zeroes, (D>0) is required. For irrational zeroes, (D) must not be a perfect square.

Step 3

Exam Tip

वास्तविक भिन्न शून्यकों के लिए (D>0) चाहिए। अपरिमेय शून्यकों के लिए (D) पूर्ण वर्ग नहीं होना चाहिए।

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