Question

Find the zero's of the following q.p and verify the
relation ship between zero's and coefficients.

$1. \: \: \:4x ^{2} - 4x + 1$
​

Answer 1

p(x) = 4x²-4x+1

[Here a = 4 , b = -4 and c =1]

Finding zeroes :

4x²-4x+1 = 0

4x²-2x-2x+1 = 0

2x(2x-1) - 1(2x-1) = 0

(2x-1)(2x-1) = 0

x = ½ (α) and x = ½ (β)

Verifying relationship :

-b/a = ½+½

-(-4/4) = 1

1 = 1

Then ,

c/a = ½× ½

¼ = ¼

Hence verified.