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conjugate-root MCQ Questions for Class 10

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3 questions tagged with conjugate-root.

Question 1/3 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(2+\sqrt{13}\) परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक है, तो उस बहुपद में (x) का गुणांक किस रूप में हो सकता है?

If \(2+\sqrt{13}\) is one zero of a quadratic polynomial with rational coefficients, what can the coefficient of (x) be?

Explanation opens after your attempt
Correct Answer

A. (-4)

Step 1

Concept

The other zero will be \(2-\sqrt{13}\), so the sum is (4). In a monic polynomial, the coefficient of (x) will be (-4).

Step 2

Why this answer is correct

The correct answer is A. (-4). The other zero will be \(2-\sqrt{13}\), so the sum is (4). In a monic polynomial, the coefficient of (x) will be (-4).

Step 3

Exam Tip

दूसरा शून्यक \(2-\sqrt{13}\) होगा, इसलिए योग (4) है। एकक बहुपद में (x) का गुणांक (-4) होगा।

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Question 2/3 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि (p(x)=x-2+ax+7) का एक शून्यक \(\sqrt{7}\) है और (a) परिमेय है, तो (a) क्या होगा?

If one zero of (p(x)=x-2+ax+7) is \(\sqrt{7}\) and (a) is rational, what is (a)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

The other zero will be \(-\sqrt{7}\), so the sum is (0) and (a=-0=0). With rational coefficients, take the conjugate zero.

Step 2

Why this answer is correct

The correct answer is A. (0). The other zero will be \(-\sqrt{7}\), so the sum is (0) and (a=-0=0). With rational coefficients, take the conjugate zero.

Step 3

Exam Tip

दूसरा शून्यक \(-\sqrt{7}\) होगा, इसलिए योग (0) और (a=-0=0) है। परिमेय गुणांक में संयुग्मी शून्यक लेना जरूरी है।

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Question 3/3 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि \(2+\sqrt{3}\) किसी परिमेय गुणांकों वाले द्विघात बहुपद का शून्यक है, तो दूसरा शून्यक क्या होगा?

If \(2+\sqrt{3}\) is a zero of a quadratic polynomial with rational coefficients, what will the other zero be?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

With rational coefficients, the conjugate of an irrational zero is also a zero. So \(2-\sqrt{3}\) will be the other zero.

Step 2

Why this answer is correct

The correct answer is A. \(2-\sqrt{3}\). With rational coefficients, the conjugate of an irrational zero is also a zero. So \(2-\sqrt{3}\) will be the other zero.

Step 3

Exam Tip

परिमेय गुणांकों में अपरिमेय शून्यक का संयुग्मी भी शून्यक होता है। इसलिए \(2-\sqrt{3}\) दूसरा शून्यक होगा।

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