यदि \(x^2-9x+n=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=45\), तो (n) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-9x+n=0\) and \(\alpha^2+\beta^2=45\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=9\) and \(\alpha\beta=n\). From (81-2n=45), we get (n=18).
Step 2
Why this answer is correct
The correct answer is B. (18). Here \(\alpha+\beta=9\) and \(\alpha\beta=n\). From (81-2n=45), we get (n=18).
Step 3
Exam Tip
\(\alpha+\beta=9\) और \(\alpha\beta=n\) है। (81-2n=45) से (n=18) मिलता है।
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यदि \(x^2-8x+n=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=40\), तो (n) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-8x+n=0\) and \(\alpha^2+\beta^2=40\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=n\). From \(\alpha^2+\beta^2=64-2n=40\), we get (n=12).
Step 2
Why this answer is correct
The correct answer is B. (12). Here \(\alpha+\beta=8\) and \(\alpha\beta=n\). From \(\alpha^2+\beta^2=64-2n=40\), we get (n=12).
Step 3
Exam Tip
\(\alpha+\beta=8\) और \(\alpha\beta=n\) है। \(\alpha^2+\beta^2=64-2n=40\) से (n=12) मिलता है।
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यदि \(x^2-6x+n=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=20\), तो (n) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-6x+n=0\) and \(\alpha^2+\beta^2=20\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=6\) and \(\alpha\beta=n\). From (36-2n=20), we get (n=8).
Step 2
Why this answer is correct
The correct answer is A. (8). Here \(\alpha+\beta=6\) and \(\alpha\beta=n\). From (36-2n=20), we get (n=8).
Step 3
Exam Tip
\(\alpha+\beta=6\) और \(\alpha\beta=n\) है। (36-2n=20) से (n=8) मिलता है।
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यदि \(x^2-5x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^2+\beta^2\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-5x+1=0\), what is \(\alpha^2+\beta^2\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). Thus \(\alpha^2+\beta^2=25-2=23\).
Step 2
Why this answer is correct
The correct answer is C. (23). Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). Thus \(\alpha^2+\beta^2=25-2=23\).
Step 3
Exam Tip
\(\alpha+\beta=5\) और \(\alpha\beta=1\) है। इसलिए \(\alpha^2+\beta^2=25-2=23\)।
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यदि \(a=3+\sqrt{7}\) और \(b=3-\sqrt{7}\) हैं तो \(a^2+b^2\) का मान क्या है?
If \(a=3+\sqrt{7}\) and \(b=3-\sqrt{7}\), what is the value of \(a^2+b^2\)?
Explanation opens after your attempt
Step 1
Concept
On adding the two squares the radical terms cancel and the result is (32). Identify cancelling terms in conjugates.
Step 2
Why this answer is correct
The correct answer is A. (32). On adding the two squares the radical terms cancel and the result is (32). Identify cancelling terms in conjugates.
Step 3
Exam Tip
दोनों वर्ग जोड़ने पर जड़ वाले पद कट जाते हैं और (32) मिलता है। संयुग्मी संख्याओं में कटने वाले पद पहचानें।
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