Question

Find the zeroes of the quadratic polynomials 8x²– 22x – 21 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = 8x² – 22x – 21

By splitting the middle term, we get

f(x) = 8x² – 28x + 6x – 21

= 4x(2x – 7) + 3(2x – 7)

= (4x + 3) (2x – 7)

On putting f(x) = 0 , we get

(4x + 3) (2x – 7) = 0

⇒ 4x + 3 = 0 or 2x – 7 = 0

x = -3/4 or x = 7/2

Thus, the zeroes of the given polynomial 8x² – 22x – 21 are -3/4 and 7/2.

Verification

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