If one of the zeroes of the cubic polynomial x^{3} + ax^{2} + 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) = x^{3} + ax^{2} + 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)^{2}a + (- 1)b + c = 0

= - 1 + a - b + c = 0

= c = 1 - a + b

Product of zeroes = - (constant term) ÷ coefficient of x^{3} i.e.

Product of zeroes = - c

αβγ = - c

= βγ = c

= βγ = 1 - a + b

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