Question

Find a cubic polynomial with the sum sum of the product of its zeros taken two at a time and product of its zeros as 3,-1$-3respectily

Answer 1

Hi friend,

Let α,β,γ, are the zeroes of the cubic polynomial.

Sum of zeroes=α+β+γ=3
Sum of the product of zeroes taken two at a time =αβ+βγ+αγ= -1
Product of zeroes=αβγ= -3

A cubic polynomial which has three zeroes is in the form,
x³-x²(α+β+γ)+x(αβ+βγ+αγ)-αβγ

Therefore,the required cubic polynomial is
x³-x²(3)+x(-1)-(-3)
=x³-3x²-x+3

Hope this helps......

Answer 2

Hope this answer is helpful