Concept-wise Practice

roots-relation MCQ Questions for Class 10

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

Practice Questions

7 questions tagged with roots-relation.

यदि \(x^2+px+64=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+64=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \(12\sqrt{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=64\) gives \(r=4\sqrt{2}\), and \(p=3r=12\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 2

Why this answer is correct

The correct answer is A. \(12\sqrt{2}\). Let the roots be (-r) and (-2r), then \(2r^2=64\) gives \(r=4\sqrt{2}\), and \(p=3r=12\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=64\) से \(r=4\sqrt{2}\) और \(p=3r=12\sqrt{2}\) है। परीक्षा में दोनों मूलों के चिन्ह ध्यान से रखें।

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यदि \(x^2+px+49=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+49=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{21\sqrt{2}}{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=49\) and \(p=3r=\frac{21\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{21\sqrt{2}}{2}\). Let the roots be (-r) and (-2r), then \(2r^2=49\) and \(p=3r=\frac{21\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=49\) और \(p=3r=\frac{21\sqrt{2}}{2}\) है। परीक्षा में हर को परिमेय बनाना न भूलें।

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यदि \(x^2+px+36=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+36=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \(9\sqrt{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=36\) gives \(r=3\sqrt{2}\), and \(p=3r=9\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 2

Why this answer is correct

The correct answer is A. \(9\sqrt{2}\). Let the roots be (-r) and (-2r), then \(2r^2=36\) gives \(r=3\sqrt{2}\), and \(p=3r=9\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=36\) से \(r=3\sqrt{2}\) और \(p=3r=9\sqrt{2}\) है। परीक्षा में दोनों मूलों के चिन्ह ध्यान से रखें।

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यदि \(x^2+px+25=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+25=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{15\sqrt{2}}{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=25\) and \(p=3r=\frac{15\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{15\sqrt{2}}{2}\). Let the roots be (-r) and (-2r), then \(2r^2=25\) and \(p=3r=\frac{15\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=25\) और \(p=3r=\frac{15\sqrt{2}}{2}\) है। परीक्षा में हर को परिमेय बनाना न भूलें।

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यदि \(x^2+px+16=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+16=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \(6\sqrt{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=16\) gives \(r=2\sqrt{2}\), and \(p=3r=6\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 2

Why this answer is correct

The correct answer is A. \(6\sqrt{2}\). Let the roots be (-r) and (-2r), then \(2r^2=16\) gives \(r=2\sqrt{2}\), and \(p=3r=6\sqrt{2}\). In exams, keep signs of both roots carefully.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=16\) से \(r=2\sqrt{2}\) और \(p=3r=6\sqrt{2}\) है। परीक्षा में दोनों मूलों के चिन्ह ध्यान से रखें।

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यदि \(x^2+px+9=0\) का एक मूल दूसरे का दुगुना है और दोनों ऋणात्मक हैं, तो (p) का सही सरल मान क्या है?

If one root of \(x^2+px+9=0\) is double the other and both are negative, what is the correct simplified value of (p)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{9\sqrt{2}}{2}\)

Step 1

Concept

\(\frac{9}{\sqrt{2}}\) simplifies to \(\frac{9\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{9\sqrt{2}}{2}\). \(\frac{9}{\sqrt{2}}\) simplifies to \(\frac{9\sqrt{2}}{2}\). In exams, do not forget to rationalize the denominator.

Step 3

Exam Tip

\(\frac{9}{\sqrt{2}}\) को सरल करने पर \(\frac{9\sqrt{2}}{2}\) मिलता है। परीक्षा में हर को परिमेय बनाना न भूलें।

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यदि \(x^2+px+9=0\) का एक मूल दूसरे मूल का दुगुना है और दोनों ऋणात्मक हैं, तो (p) क्या होगा?

If one root of \(x^2+px+9=0\) is double the other and both are negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. \(3\sqrt{2}\)

Step 1

Concept

Let the roots be (-r) and (-2r), then \(2r^2=9\) and the sum is (-3r), so \(p=3r=\frac{9}{\sqrt{2}}\). In exams, assume the roots and form equations carefully.

Step 2

Why this answer is correct

The correct answer is A. \(3\sqrt{2}\). Let the roots be (-r) and (-2r), then \(2r^2=9\) and the sum is (-3r), so \(p=3r=\frac{9}{\sqrt{2}}\). In exams, assume the roots and form equations carefully.

Step 3

Exam Tip

मूलों को (-r) और (-2r) मानें, तो \(2r^2=9\) और योग (-3r) है, इसलिए \(p=3r=3\sqrt{\frac{9}{2}}\) नहीं बल्कि \(r=\frac{3}{\sqrt{2}}\), अतः \(p=\frac{9}{\sqrt{2}}\) होता है। परीक्षा में ऐसे प्रश्नों में मानकर समीकरण बनाएं।

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