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Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively. 4, 1 - Mathematics

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Question

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

4, 1

Sum
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Solution

Given: α + β = 4, αβ = 1

α + β = `(-b)/a = 4/1` and αβ = `c/a = 1`

By comparison a = 1, b = -4 and c = 1

Hence, after substituting the values in ax2 + bx + c,

ax2 + bx + c = (1)x2 + (-4)x + 1

= x2 – 4x + 1

Hence, the quadratic polynomial is x2 – 4x + 1.

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Chapter 2: Polynomials - Exercise 2.2 [Page 33]

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NCERT Mathematics [English] Class 10
Chapter 2 Polynomials
Exercise 2.2 | Q 2.6 | Page 33

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