Question 1/3
Expert Mathematics
Chapter 2: 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?
#polynomial-from-zero
#conjugate-roots
#irrational-numbers
A \(x^2-10x+4\)
B \(x^2+10x+4\)
C \(x^2-5x+21\)
D \(x^2-10x+46\)
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
Chapter 2: 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?
#polynomial-from-zero
#conjugates
#irrational-roots
A \(x^2-6x+1\)
B \(x^2+6x+1\)
C \(x^2-3x+8\)
D \(x^2-6x+17\)
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
Chapter 2: 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?
#polynomial-from-zero
#conjugates
#irrational-numbers
A \(x^2-10x+1\)
B \(x^2+10x+1\)
C \(x^2-5x+6\)
D \(x^2-10x+49\)
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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