Question

Find the polynomial whose sum and product of zeroes are 1/2 and -1/4

Answer 1

The required polynomial is :

x^2 - (1/2)x + (-1/4) = 0

4x^2 - 2x - 1 = 0

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Answer 2

$\textbf{Solution:}$

Given

sum of zeroes = 1 / 2

alpha + beta = 1 / 2

And

Product of zeroes = - 1 / 4

alpha × beta = - 1 / 4

Required polynomial = x^2 - ( alpha + beta )x + alpha.beta

= x^2 - 1 / 2x - 1 / 4

= 2x^2 - x - 2 / 4

= 8x^2 - 4x - 2

Hence Ans:

$\boxed{8x^2 - 4x - 2}$