The number of quadratic polynomials having zeros –5 and –3 is:
(4)
Given: zeros of the polynomial are –5 and –3.
Polynomials having zeros –5 and –3 are given by p(x) = k(x + 5)(x + 3).
⇒ p(x) = k(x² + 8x + 15), where k is any real constant.
∴ k can have infinitely many values. So, number of possible polynomials is infinitely many.