Question

If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is - 1, then the product of the other two zeroes is 

A. b - a + 1  

B. b - a - 1 

C. a - b + 1 

D. a - b - 1

Answer 1

A. b - a + 1

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