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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.
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Solution
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
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