Question

Find the zeroes of the quadratic polynomials x² – 2x – 8 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = x² – 2x – 8

By splitting the middle term, we get

f(x) = x² – 4x + 2x – 8 [∵ – 2 = 2 – 4 and 2×4 = 8]

= x(x – 4) + 2(x – 4)

= (x + 2) (x – 4)

On putting f(x) = 0, we get

(x + 2) (x – 4) = 0

⇒ x + 2 = 0 or x – 4 = 0

⇒x = – 2 or x = 4

Thus, the zeroes of the given polynomial x² – 2x – 8 are – 2 and 4

Verification

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