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3 results found for "irrational-real" in Class 10.

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

कौन सा बहुपद परिमेय गुणांकों वाला है और उसके दोनों शून्यक अपरिमेय वास्तविक हैं?

Which polynomial has rational coefficients and both zeroes irrational real?

Explanation opens after your attempt
Correct Answer

A. \(x^2-8x+3\)

Step 1

Concept

For \(x^2-8x+3\), (D=64-12=52), positive and not a perfect square. The other options give equal rational, non-real, or rational zeroes.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-8x+3\). For \(x^2-8x+3\), (D=64-12=52), positive and not a perfect square. The other options give equal rational, non-real, or rational zeroes.

Step 3

Exam Tip

\(x^2-8x+3\) के लिए (D=64-12=52), जो धनात्मक अपूर्ण वर्ग है। बाकी विकल्पों में शून्यक समान परिमेय, अवास्तविक या परिमेय हैं।

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

यदि (p(x)=x-2-9x+14) और (q(x)=x-2-9x+15) हैं, तो शून्यकों के प्रकार के बारे में सही कथन कौन सा है?

If (p(x)=x-2-9x+14) and (q(x)=x-2-9x+15), which statement about the types of zeroes is correct?

Explanation opens after your attempt
Correct Answer

A. (p(x)) के शून्यक परिमेय हैं और (q(x)) के शून्यक अपरिमेय वास्तविक हैंZeroes of (p(x)) are rational and zeroes of (q(x)) are irrational real

Step 1

Concept

For (p(x)), (D=81-56=25), a perfect square, so the zeroes are rational. For (q(x)), (D=81-60=21), positive but not a perfect square, so the zeroes are irrational real.

Step 2

Why this answer is correct

The correct answer is A. (p(x)) के शून्यक परिमेय हैं और (q(x)) के शून्यक अपरिमेय वास्तविक हैं / Zeroes of (p(x)) are rational and zeroes of (q(x)) are irrational real. For (p(x)), (D=81-56=25), a perfect square, so the zeroes are rational. For (q(x)), (D=81-60=21), positive but not a perfect square, so the zeroes are irrational real.

Step 3

Exam Tip

(p(x)) के लिए (D=81-56=25) पूर्ण वर्ग है, इसलिए शून्यक परिमेय हैं। (q(x)) के लिए (D=81-60=21) धनात्मक अपूर्ण वर्ग है, इसलिए शून्यक अपरिमेय वास्तविक हैं।

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

यदि (p(x)=x-2-k) के शून्यक अपरिमेय वास्तविक हैं, तो (k) के लिए सही शर्त कौन सी है?

If the zeroes of (p(x)=x-2-k) are irrational real, which condition on (k) is correct?

Explanation opens after your attempt
Correct Answer

B. (k) धनात्मक हो लेकिन पूर्ण वर्ग न हो(k) is positive but not a perfect square

Step 1

Concept

The zeroes are \(x=\pm\sqrt{k}\). They are irrational real when (k>0) and (k) is not a perfect square.

Step 2

Why this answer is correct

The correct answer is B. (k) धनात्मक हो लेकिन पूर्ण वर्ग न हो / (k) is positive but not a perfect square. The zeroes are \(x=\pm\sqrt{k}\). They are irrational real when (k>0) and (k) is not a perfect square.

Step 3

Exam Tip

शून्यक \(x=\pm\sqrt{k}\) हैं। ये अपरिमेय वास्तविक तभी होंगे जब (k>0) और (k) पूर्ण वर्ग न हो।

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