Question

Find the zeroes of the quadratic polynomial 5x² – 8x – 4 and verify the relationship between the zeroes and the coefficients of the polynomial.

Answer 1

Let f(x) = 5x² – 8x – 4

By splitting the middle term, we get

f(x) = 5x² – 10x + 2x – 4

= 5x(x – 2) + 2(x – 2)

= (5x + 2) (x – 2)

On putting f(x) = 0 we get

(5x + 2) (x – 2) = 0

⇒ 5x + 2 = 0 or x – 2 = 0

x = -2/5 or x = 2

Thus, the zeroes of the given polynomial5x² – 8x – 4 are -2/5 and 2

Verification

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