If one of the zeroes of the cubic polynomial x3 + px2 + qx + r is -1, then . . .

Question : If one of the zeroes of the cubic polynomial x³ + px² + qx + r is -1, then the product of the other two zeroes is 

a) p+q+1

b) p-q-1

c) q-p+1

d) q-p-1

Doubt by Zoha

Solution :

α = -1 (Given)
x³ + px² + qx + r

Here

a=1

b=p

c=q

d=r

α+β+γ=-b/a
α+β+(-1)=-p/1
α+β = -p+1 — (1)

Also, 
αβ+βγ+γα=c/a
αβ+β(-1)+(-1)α=q/1
αβ-(β+α)=q
αβ-(α+β)=q
αβ-(-p+1)=q [Using equation (1)]
αβ+p-1=q 
αβ = q-p+1

Hence, c) q-p+1, is the correct option.