Question

Find the zeroes of the quadratic polynomial 4s² – 4s + 1 and verify the relationship between the zeroes and the coefficients.

Answer 1

P(s) = 4s² – 4s + 1

4s² – 2s – 2s + 1 = 0

2s(2s – 1) – 1(2s – 1) = 0

(2s – 1) (2s – 1) = 0

s = `1/2`, s = `1/2`

a = 4, b = – 4, c = 1, ∝ = `1/2`, β = `1/2`

∝ + β = `(-b)/a`, ∝β = `c/a`

`1/2 + 1/2 = (-4)/4, (1/2)(1/2) = 1/4` 

`(1 + 1)/2 = (+4)/4, 1/4 = 1/4`

`2/2` = 1

1 = 1