If α,β,γ are the zeroes of a cubic polynomial ax3+bx2+cx+d, then the product of zeroes is
Ggiven that
p(x)=ax3+bx2+cx+d .........(1) where a≠0 is a cubic polynomial
And α,β,γ are the zeroes of the polynomial p(x)
We can also write the polynomial in this way
p(x)=(x−α)(x−β)(x−γ)
⇒p(x)=x3−(α+β+γ)x2+(αβ+βγ+γα)x−αβγ .............(2)
Equations (1) and (2) are same
Comparing the coefficients
a1=b−α−β−γ=cαβ+βγ+γα=d−αβγ
On solving we get the following results
α+β+γ=−ba= Sum of the roots
αβ+βγ+γα=ca