Concept-wise Practice

negative_roots MCQ Questions for Class 10

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

Practice Questions

6 questions tagged with negative_roots.

यदि (a< b) और (a,b) संख्या रेखा पर \(a=-\sqrt{10}\), \(b=-\sqrt{m}\) हैं, तो (m) के लिए कौन सा मान सही हो सकता है?

If (a< b) and (a,b) on the number line are \(a=-\sqrt{10}\), \(b=-\sqrt{m}\), which value of (m) can be correct?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

For \( -\sqrt{10}<-\sqrt{m}\), we need \( \sqrt{10}>\sqrt{m}\), so (m<10). Inequality reverses with negative roots.

Step 2

Why this answer is correct

The correct answer is A. (8). For \( -\sqrt{10}<-\sqrt{m}\), we need \( \sqrt{10}>\sqrt{m}\), so (m<10). Inequality reverses with negative roots.

Step 3

Exam Tip

\( -\sqrt{10}<-\sqrt{m}\) के लिए \( \sqrt{10}>\sqrt{m}\), इसलिए (m<10)। ऋणात्मक मूलों में असमानता उलटती है।

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संख्या रेखा पर \( -\sqrt{7} \) किस दो लगातार पूर्णांकों के बीच स्थित है?

Between which two consecutive integers is \( -\sqrt{7} \) located on the number line?

Explanation opens after your attempt
Correct Answer

A. ( -3) और (-2)( -3) and (-2)

Step 1

Concept

Since \(2<\sqrt{7}<3\), we have \(-3<-\sqrt{7}<-2\). For negative numbers, remember the order reverses.

Step 2

Why this answer is correct

The correct answer is A. ( -3) और (-2) / ( -3) and (-2). Since \(2<\sqrt{7}<3\), we have \(-3<-\sqrt{7}<-2\). For negative numbers, remember the order reverses.

Step 3

Exam Tip

क्योंकि \(2<\sqrt{7}<3\), इसलिए \(-3<-\sqrt{7}<-2\)। ऋणात्मक संख्या में क्रम उलटने पर ध्यान रखें।

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संख्या रेखा पर \(-\sqrt{25}\) और \(-\sqrt{36}\) में कौन सा बिंदु दाईं ओर होगा?

On the number line, which point will be to the right, \(-\sqrt{25}\) or \(-\sqrt{36}\)?

Explanation opens after your attempt
Correct Answer

A. \(-\sqrt{25}\)

Step 1

Concept

\(-\sqrt{25}=-5\) and \(-\sqrt{36}=-6\), so (-5) is to the right. Among negatives, the one with smaller magnitude is greater.

Step 2

Why this answer is correct

The correct answer is A. \(-\sqrt{25}\). \(-\sqrt{25}=-5\) and \(-\sqrt{36}=-6\), so (-5) is to the right. Among negatives, the one with smaller magnitude is greater.

Step 3

Exam Tip

\(-\sqrt{25}=-5\) और \(-\sqrt{36}=-6\), इसलिए (-5) दाईं ओर है। ऋणात्मक संख्याओं में कम परिमाण वाली संख्या बड़ी होती है।

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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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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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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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