Search: symmetric-expression

Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(x^2-2x-11\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2+\beta^2+\alpha\beta\) क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-2x-11\), what is \(\alpha^2+\beta^2+\alpha\beta\)?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

\(\alpha+\beta=2\) and \(\alpha\beta=-11\), so (\alpha^-2+\beta^-2+\alpha\beta=\(\alpha+\beta\)²-\alpha\beta=4+11=15). Sum and product are enough for symmetric expressions.

Step 2

Why this answer is correct

The correct answer is A. (15). \(\alpha+\beta=2\) and \(\alpha\beta=-11\), so (\alpha^-2+\beta^-2+\alpha\beta=\(\alpha+\beta\)²-\alpha\beta=4+11=15). Sum and product are enough for symmetric expressions.

Step 3

Exam Tip

\(\alpha+\beta=2\) और \(\alpha\beta=-11\), इसलिए (\alpha^-2+\beta^-2+\alpha\beta=\(\alpha+\beta\)²-\alpha\beta=4+11=15)। सममित व्यंजकों में योग और गुणनफल काफी होते हैं।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि (p(x)=x^-2-2x-4) है, तो इसके शून्यकों का वर्गों का योग क्या है?

If (p(x)=x^-2-2x-4), what is the sum of squares of its zeroes?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(\alpha+\beta=2\) and \(\alpha\beta=-4\), so (\alpha^-2+\beta^-2=2²-2(-4)=12). Symmetric values can be found without finding the zeroes.

Step 2

Why this answer is correct

The correct answer is A. (12). \(\alpha+\beta=2\) and \(\alpha\beta=-4\), so (\alpha^-2+\beta^-2=2²-2(-4)=12). Symmetric values can be found without finding the zeroes.

Step 3

Exam Tip

\(\alpha+\beta=2\) और \(\alpha\beta=-4\), इसलिए (\alpha^-2+\beta^-2=2²-2(-4)=12)। शून्यक निकाले बिना सममित मान निकाल सकते हैं।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(\alpha=5+\sqrt{6}\) और \(\beta=5-\sqrt{6}\), तो \(\alpha^2+\beta^2\) का मान क्या है?

If \(\alpha=5+\sqrt{6}\) and \(\beta=5-\sqrt{6}\), what is the value of \(\alpha^2+\beta^2\)?

Explanation opens after your attempt

Correct Answer

A. (62)

Step 1

Concept

\(\alpha+\beta=10\) and \(\alpha\beta=25-6=19\), so \(\alpha^2+\beta^2=100-38=62\). Use (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta).

Step 2

Why this answer is correct

The correct answer is A. (62). \(\alpha+\beta=10\) and \(\alpha\beta=25-6=19\), so \(\alpha^2+\beta^2=100-38=62\). Use (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta).

Step 3

Exam Tip

\(\alpha+\beta=10\) और \(\alpha\beta=25-6=19\), इसलिए \(\alpha^2+\beta^2=100-38=62\)। पहचान (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) उपयोग करें।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि \(\alpha=3+\sqrt{11}\) और \(\beta=3-\sqrt{11}\), तो \(\alpha^2+\beta^2\) क्या है?

If \(\alpha=3+\sqrt{11}\) and \(\beta=3-\sqrt{11}\), what is \(\alpha^2+\beta^2\)?

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

\(\alpha+\beta=6\) and \(\alpha\beta=9-11=-2\), so (\alpha^-2+\beta^-2=36-2(-2)=40). The identity (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) is useful.

Step 2

Why this answer is correct

The correct answer is A. (40). \(\alpha+\beta=6\) and \(\alpha\beta=9-11=-2\), so (\alpha^-2+\beta^-2=36-2(-2)=40). The identity (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) is useful.

Step 3

Exam Tip

\(\alpha+\beta=6\) और \(\alpha\beta=9-11=-2\), इसलिए (\alpha^-2+\beta^-2=36-2(-2)=40)। पहचान (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) उपयोगी है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(\alpha=2+\sqrt{7}\) और \(\beta=2-\sqrt{7}\), तो \(\alpha^2+\beta^2\) क्या है?

If \(\alpha=2+\sqrt{7}\) and \(\beta=2-\sqrt{7}\), what is \(\alpha^2+\beta^2\)?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

\(\alpha+\beta=4\) and \(\alpha\beta=4-7=-3\). Thus (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=16+6=22).

Step 2

Why this answer is correct

The correct answer is A. (22). \(\alpha+\beta=4\) and \(\alpha\beta=4-7=-3\). Thus (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=16+6=22).

Step 3

Exam Tip

\(\alpha+\beta=4\) और \(\alpha\beta=4-7=-3\)। इसलिए (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta=16+6=22)।

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Search Class 10 Questions

यदि \(x^2-2x-11\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2+\beta^2+\alpha\beta\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2-2x-4) है, तो इसके शून्यकों का वर्गों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(\alpha=5+\sqrt{6}\) और \(\beta=5-\sqrt{6}\), तो \(\alpha^2+\beta^2\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(\alpha=3+\sqrt{11}\) और \(\beta=3-\sqrt{11}\), तो \(\alpha^2+\beta^2\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(\alpha=2+\sqrt{7}\) और \(\beta=2-\sqrt{7}\), तो \(\alpha^2+\beta^2\) क्या है?

Concept

Why this answer is correct

Exam Tip

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यदि (p(x)=x^-2-2x-4) है, तो इसके शून्यकों का वर्गों का योग क्या है?