Question

find a cubic polynomial whose sum of zeroes and sum of the product of its zeroes , product of its zeroes as 3,-1and-3. respectively.

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Answer 1

Given :-

Sum of zeroes = 3

Sum of product of zeroes = -1

Product of zeroes = -3

To Find :-

Cubic polynomial

Solution :-

We know that

Sum = α + β + γ

Sum = 3

Product = αβγ

Product = 3

Sum of product of zeroes = αβ + βγ + αγ

Sum of product of zeroes = -1

Standard form of cubic polynomial = x³ - (α + β + γ)x² + (αβ + βγ + αγ)x - αβγ

Cubic polynomial = x³ - (3)x² + (-1)x - (3)

Cubic polynomial = x³ - 3x² - x - 3