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polynomial-from-zero MCQ Questions for Class 10

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3 questions tagged with polynomial-from-zero.

Question 1/3 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि \(5+\sqrt{21}\) किसी परिमेय गुणांक वाले द्विघात बहुपद का शून्यक है, तो उस बहुपद का एक संभव रूप कौन सा है?

If \(5+\sqrt{21}\) is a zero of a quadratic polynomial with rational coefficients, which is one possible form of that polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+4\)

Step 1

Concept

The other zero will be \(5-\sqrt{21}\). Sum (10) and product (25-21=4) give the polynomial \(x^2-10x+4\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+4\). The other zero will be \(5-\sqrt{21}\). Sum (10) and product (25-21=4) give the polynomial \(x^2-10x+4\).

Step 3

Exam Tip

दूसरा शून्यक \(5-\sqrt{21}\) होगा। योग (10) और गुणनफल (25-21=4) से बहुपद \(x^2-10x+4\) बनता है।

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

यदि \(x=3+\sqrt{8}\), तो (x) किस द्विघात बहुपद का शून्यक हो सकता है?

If \(x=3+\sqrt{8}\), which quadratic polynomial can have (x) as a zero?

Explanation opens after your attempt
Correct Answer

A. \(x^2-6x+1\)

Step 1

Concept

The companion zero is \(3-\sqrt{8}\). Sum (6) and product (9-8=1) form \(x^2-6x+1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-6x+1\). The companion zero is \(3-\sqrt{8}\). Sum (6) and product (9-8=1) form \(x^2-6x+1\).

Step 3

Exam Tip

साथी शून्यक \(3-\sqrt{8}\) है। योग (6) और गुणनफल (9-8=1) से बहुपद \(x^2-6x+1\) बनता है।

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Question 3/3 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(x=5+2\sqrt{6}\), तो (x) किस द्विघात बहुपद का शून्यक हो सकता है जिसके गुणांक परिमेय हैं?

If \(x=5+2\sqrt{6}\), which quadratic polynomial with rational coefficients can have (x) as a zero?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+1\)

Step 1

Concept

The companion zero is \(5-2\sqrt{6}\), with sum (10) and product (25-24=1). In exams form the polynomial using the conjugate.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+1\). The companion zero is \(5-2\sqrt{6}\), with sum (10) and product (25-24=1). In exams form the polynomial using the conjugate.

Step 3

Exam Tip

साथी शून्यक \(5-2\sqrt{6}\) होगा, योग (10) और गुणनफल (25-24=1) है। परीक्षा में संयुग्मी लेकर बहुपद बनाएं।

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