Question

If one of the zeroes of the cubic polynomial `x^3 + ax^2 + bx + c` is `-1`,then find the product of other two zeroes.
A. `a - b - 1`
B. ` b - a - 1`
C. ` 1 - a + b`
D. ` 1 + a - b`

Answer 1

Correct Answer - C
Since -1 is a zeros of `x^(3)+ax^(2)+bx+c`, we have
`(-1)^(3)+a xx(-1)^(2)+b xx(-1)+c = 0 rArr a -b+c-1=0 rArr c =1 - a+b.`
Also, product of all zeros is given by
`alpha beta xx(-1) =- c rArr alpha beta = c rArr alpha beta = 1-a+b.`