Question

Find the zeroes of the quadratic polynomials px² + (2q – p²)x – 2pq, p ≠ 0 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = px² + (2q – p²)x – 2pq

f(x) = px² + 2qx – p² x – 2pq

= x(px + 2q) – p(px + 2q)

= (x – p) (px + 2q)

On putting f(x) = 0, we get

(x – p) (px + 2q) = 0

⇒ x – p = 0 or px + 2q = 0

⇒x = p or x = -2q/p

Thus, the zeroes of the given polynomial px² + (2q – p²)x – 2pq are p and -2q/p.

Verification

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