Question

find the zeros of x square -x+1/4and verify the relationship between zeros and coefficient

Answer 1

x^2 - x + 1/4 = 0
4x^2 - 4x + 1 = 0 × 4 [ by taking L. C. M ]
4x^2 - 2x - 2x + 1 = 0
2x ( 2x - 1) -1 ( 2x - 1) = 0
(2x - 1) (2x - 1)
α = 1/2
β = 1/2

α + β = (-b)/a
1/2 + 1/2 = 1/1
4/4 = 1
1 = 1

αβ = c/a
1/2 × 1/2 = 1/4 /1
1/4 = 1/4

Answer 2

let,p (x)=x^2-x+1/4
= 4x^2-4x+1
= 4x^2-2x -2x +1
=2x (2x-1)-1 (2x-1)
= (2x-1)(2x-1)
since p (x)= 0
then (2x-1)(2x-1)=0
therefore x=1/2 and x=1/2
let alpha=1/2 and beta =1/2
then (alpha+beta)= 2/2=1
and (alpha×beta)=1/4