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negative_roots MCQ Questions for Class 10

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3 questions tagged with negative_roots.

Question 1/3 Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2+4x+c=0\) की दोनों जड़ें वास्तविक और ऋणात्मक हैं, तो कौन-सी शर्त पर्याप्त और आवश्यक है?

If both roots of \(x^2+4x+c=0\) are real and negative, which condition is necessary and sufficient?

Explanation opens after your attempt
Correct Answer

A. \(0<c\le4\)

Step 1

Concept

The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, \(16-4c\ge0\), hence \(0<c\le4\).

Step 2

Why this answer is correct

The correct answer is A. \(0<c\le4\). The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, \(16-4c\ge0\), hence \(0<c\le4\).

Step 3

Exam Tip

योग (-4) पहले से ऋणात्मक है और गुणनफल धनात्मक चाहिए, इसलिए (c>0)। वास्तविक जड़ों के लिए \(16-4c\ge0\), अतः \(0<c\le4\)।

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Question 2/3 Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x^2+px+18=0\) के मूलों का अनुपात (1:2) है और दोनों ऋणात्मक हैं तो (p) क्या होगा?

If roots of \(x^2+px+18=0\) are in the ratio (1:2) and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. (9)

Step 1

Concept

The roots are (-3) and (-6) because the product is (18). Their sum is (-9), so (p=9).

Step 2

Why this answer is correct

The correct answer is A. (9). The roots are (-3) and (-6) because the product is (18). Their sum is (-9), so (p=9).

Step 3

Exam Tip

मूल (-3) और (-6) होंगे क्योंकि गुणनफल (18) है। उनका योग (-9) है इसलिए (p=9) है।

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Question 3/3 Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2+px+12=0\) के मूलों का अनुपात (1:3) है और दोनों ऋणात्मक हैं तो (p) क्या होगा?

If roots of \(x^2+px+12=0\) are in the ratio (1:3) and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

The roots are (-2) and (-6) because the product is (12). Their sum is (-8), so (-p=-8) gives (p=8).

Step 2

Why this answer is correct

The correct answer is A. (8). The roots are (-2) and (-6) because the product is (12). Their sum is (-8), so (-p=-8) gives (p=8).

Step 3

Exam Tip

मूल (-2) और (-6) होंगे क्योंकि गुणनफल (12) है। उनका योग (-8) है इसलिए (-p=-8) से (p=8) है।

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