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2 results found for "monic-polynomial" in Class 10.

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

यदि शून्यक \(\frac{3+\sqrt{5}}{2}\) और \(\frac{3-\sqrt{5}}{2}\) हैं, तो एकक बहुपद क्या है?

If the zeroes are \(\frac{3+\sqrt{5}}{2}\) and \(\frac{3-\sqrt{5}}{2}\), what is the monic polynomial?

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Correct Answer

A. \(x^2-3x+1\)

Step 1

Concept

The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x+1\). The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).

Step 3

Exam Tip

योग (3) और गुणनफल \(\frac{9-5}{4}=1\) है। इसलिए बहुपद \(x^2-3x+1\) है।

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

यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?

If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.

Step 2

Why this answer is correct

The correct answer is A. \(-3\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.

Step 3

Exam Tip

\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है।

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