If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is - 1, then the product of the other two zeroes is
let α, β & γ be the zeroes of the polynomial p(x) = x3 + ax2 + bx + c and
α = - 1 (given)
Zeroes of a polynomial is all the values of x at which the polynomial is equal to zero.
i.e. p (α) = p(- 1) = 0
= (- 1)3 + (- 1)2a + (- 1)b + c = 0
= - 1 + a - b + c = 0
= c = 1 - a + b
Product of zeroes = - (constant term) ÷ coefficient of x3 i.e.
Product of zeroes = - c
αβγ = - c
= βγ = c
= βγ = 1 - a + b