Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively.

Answer 1

Any cubic polynomial is of the form ax³ + bx² + cx + d = x³ − sum of zeroes (x2)[product of zeroes] + sum of the products of its zeroes × - product of zeroes

= 𝑥³ − 2𝑥² + (3 − 𝑥) + 3

= k [𝑥³ − 3𝑥² − 𝑥 − 3]

k is any non-zero real numbers