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2 results found for "fractional-zeroes" in Class 10.

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

यदि किसी परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक \(\frac{3+\sqrt{5}}{2}\) है, तो दूसरा शून्यक क्या होगा?

If one zero of a quadratic polynomial with rational coefficients is \(\frac{3+\sqrt{5}}{2}\), what will be the other zero?

Explanation opens after your attempt
Correct Answer

A. \(\frac{3-\sqrt{5}}{2}\)

Step 1

Concept

With rational coefficients, the conjugate of the irrational part is also a zero. Hence \(\frac{3-\sqrt{5}}{2}\) is the other zero.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3-\sqrt{5}}{2}\). With rational coefficients, the conjugate of the irrational part is also a zero. Hence \(\frac{3-\sqrt{5}}{2}\) is the other zero.

Step 3

Exam Tip

परिमेय गुणांकों में अपरिमेय भाग का संयुग्मी भी शून्यक होता है। इसलिए \(\frac{3-\sqrt{5}}{2}\) दूसरा शून्यक है।

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

यदि शून्यक \(\frac{1+\sqrt{3}}{2}\) और \(\frac{1-\sqrt{3}}{2}\) हैं, तो उनका गुणनफल क्या है?

If the zeroes are \(\frac{1+\sqrt{3}}{2}\) and \(\frac{1-\sqrt{3}}{2}\), what is their product?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{1}{2}\)

Step 1

Concept

The product is (\frac{\(1+\sqrt{3}\)\(1-\sqrt{3}\)}{4}=\frac{1-3}{4}=-\frac{1}{2}). Use \(a^2-b\) for conjugate products.

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{1}{2}\). The product is (\frac{\(1+\sqrt{3}\)\(1-\sqrt{3}\)}{4}=\frac{1-3}{4}=-\frac{1}{2}). Use \(a^2-b\) for conjugate products.

Step 3

Exam Tip

गुणनफल (\frac{\(1+\sqrt{3}\)\(1-\sqrt{3}\)}{4}=\frac{1-3}{4}=-\frac{1}{2}) है। संयुग्मी गुणनफल में \(a^2-b\) प्रयोग करें।

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