Question

find a cubic polynomial with the sum,sum of product of its zeroes taken two at a time and the product of its zeroes respectively as given below
(a)-4,7 and 0

Answer 1

A cubic polynomial is of the form ax³+bx²+cx+d

But when the sum,sum of product of its zeroes taken two at a time and the product of its zeroes are given,it is of the form:-

x³ - (α+β+γ)x² + (αβ+βγ+αβ)x - αβγ

Here,
α+β+γ = -4

αβ+βγ+αβ = 7

αβγ = 0

The cubic polynomial is

x³ -(-4)x² + (7)x -0

x³+4x²+7x

Hope it helps