Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

4s² – 4s + 1

Answer 1

Given polynomial is 4s² – 4s + 1 

We have, 4s² – 4s + 1 

= 4s² – 2s – 2s + 1

= 2s (2s – 1) – 1(2s – 1) 

= (2s – 1) (2s – 1) 

= (2s – 1)² 

So, the value of 4s² – 4s + 1 is zero 

when 2s - 1 = 0 or s = 1/2

∴ Zeroes of the polynomial are 1/2 and 1/2

∴ Sum of the zeroes = 1/2 + 1/2 =1.

= \(-\frac{Coefficient\,of\,s}{Coefficient\,of\,s^2} = -\frac{-4}{4}=1\)

And product of the zeroes = (1/2) x (1/2) =1/4

\(=\frac{constant\,term}{coefficient\,of\,x^2}=\frac{1}{4}\)