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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि (x-2-(2a+1)x+a-2+a-6=0) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha-\beta\) का धनात्मक मान क्या होगा?

If \(\alpha,\beta\) are the roots of (x-2-(2a+1)x+a-2+a-6=0), what is the positive value of \(\alpha-\beta\)?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

Here \(\alpha+\beta=2a+1\) and \(\alpha\beta=a^2+a-6\). Since (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta=25), the positive difference is (5).

Step 2

Why this answer is correct

The correct answer is A. (5). Here \(\alpha+\beta=2a+1\) and \(\alpha\beta=a^2+a-6\). Since (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta=25), the positive difference is (5).

Step 3

Exam Tip

यहाँ \(\alpha+\beta=2a+1\) और \(\alpha\beta=a^2+a-6\) है। (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta=25), इसलिए धनात्मक अंतर (5) है।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

(x-2-(a+8)x+8a=0) के बारे में कौन-सा कथन हमेशा सही है?

Which statement is always correct about (x-2-(a+8)x+8a=0)?

Explanation opens after your attempt
Correct Answer

A. (8) हमेशा एक जड़ है(8) is always one root

Step 1

Concept

Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).

Step 2

Why this answer is correct

The correct answer is A. (8) हमेशा एक जड़ है / (8) is always one root. Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).

Step 3

Exam Tip

(x=8) रखने पर (64-8(a+8)+8a=0) मिलता है। इसलिए (8) हमेशा एक जड़ है और दूसरी जड़ (a) है।

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

यदि (2x-2-(3p+2)x+p(p+2)=0) की एक जड़ (p) है, तो दूसरी जड़ क्या होगी?

If one root of (2x-2-(3p+2)x+p(p+2)=0) is (p), what will be the other root?

Explanation opens after your attempt
Correct Answer

A. \(\frac{p+2}{2}\)

Step 1

Concept

The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{p+2}{2}\). The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).

Step 3

Exam Tip

जड़ों का गुणनफल (\frac{p(p+2)}{2}) है। एक जड़ (p) होने पर दूसरी जड़ \(\frac{p+2}{2}\) होगी।

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

(x-2-(a+6)x+6a=0) के लिए कौन-सा कथन हमेशा सत्य है?

Which statement is always true for (x-2-(a+6)x+6a=0)?

Explanation opens after your attempt
Correct Answer

B. (6) हमेशा जड़ है(6) is always a root

Step 1

Concept

Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).

Step 2

Why this answer is correct

The correct answer is B. (6) हमेशा जड़ है / (6) is always a root. Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).

Step 3

Exam Tip

(x=6) रखने पर (36-6(a+6)+6a=0) मिलता है। इसलिए (6) हमेशा एक जड़ है और दूसरी जड़ (a) है।

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

यदि (x-2-(m+2)x+3m=0) की एक जड़ (3) है, तो दूसरी जड़ क्या है?

If one root of (x-2-(m+2)x+3m=0) is (3), what is the other root?

Explanation opens after your attempt
Correct Answer

A. (m)

Step 1

Concept

Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).

Step 2

Why this answer is correct

The correct answer is A. (m). Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).

Step 3

Exam Tip

(x=3) रखने पर समीकरण हर (m) के लिए सही हो जाता है। गुणनफल (3m) है और एक जड़ (3), इसलिए दूसरी जड़ (m) है।

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