If one of the zeroes of the cubic polynomial `ax^(3) +bx^(2) +cx +d` is zero, then the product of other two zeroes is

Options

A. `(-c)/(a)`
B. `(c)/(a)`
C. 0
D. `(-b)/(a)`

Answer

B

Explanation

Let `p(x) =ax^(3) +bx^(2) +cx +d`
Given that, one of the zeroes of the cubic polynomial `p(x)` is zero.
Let `alpha, beta` and `gamma` are the zeroes of cubic polynomial `p(x)`, where `a = 0`. We known that,
Sum of product of two zeroes at a time `= (c)/(a)`
`rArr alpha beta +beta gamma +gamma alpha = (c)/(a)`
`rArr 0 xx beta +beta gamma +gamma xx 0 = (c)/(a) [ :' alpha = 0, "given"]`
`rArr 0 + beta gamma +0 =(c)/(a)`
`rArr beta gamma = (c)/(a)`
Hence, product of other two zeroes `= (c)/(a)`