Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as `2, 7, 14` respectively.

Answer 1

`Q(x)=ax^3+bx^2+cx+d`
`alpha,beta,gamma` are the zeroes
`alpha+beta+gamma=(-coefficient of x^2)/(coefficient of x^3)=-b/a=2`-(1)
`alphabeta+betagamma+gammabeta=(coefficient of x)/(coefficient of x^2)=c/a=-7`-(2)
`alphabetagamma=(-constant term)/(coefficient of x)=-d/a=-14`-(3)
if a=1
then b=-2, c=-7, d=14
`Q(x)=x^3-2x^2-7x+14`.