Question

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

Answer 1

Let f(x) = 4 s² – 4s + 1

By splitting the middle term, we get

f(x) = 4 s² – (2 – 2)s + 1 [∵ – 4 = – (2 + 2) and 2×2 = 4]

= 4 s² – 2s – 2s + 1

= 2s(2s – 1) – 1(2s – 1)

= (2s – 1) (2s – 1)

On putting f(x) = 0 , we get

(2s – 1) (2s – 1) = 0

⇒ 2s – 1 = 0 or 2s – 1 = 0

s = 1/2 or s = 1/2

Thus, the zeroes of the given polynomial 4s² – 4s + 1 are 1/2 and 1/2.

Verification

So, the relationship between the zeroes and the coefficients is verified.