Question

Find the zeroes of the quadratic polynomial 4x² – 4x – 3 and verify the relationship between the zeroes and the coefficients of the polynomial.

Answer 1

Let f(x) = 4 x² – 4x – 3

By splitting the middle term, we get

f(x) = 4 x² – 6x + 2x – 3

= 2x(2x – 3) + 1(2x – 3)

= (2x + 1) (2x – 3)

On putting f(x) = 0, we get

(2x + 1) (2x – 3) = 0

⇒ 2x + 1 = 0 or 2x – 3 = 0

x = -1/2 or x = 3/2

Thus, the zeroes of the given polynomial4x² – 4x – 3 are -1/2 and 3/2.

Verification

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