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If the sum of the two roots of x^3 + px^...

If the sum of the two roots of `x^3 + px^2 + ax + r = 0` is zero then `pq=`

A

`-r`

B

r

C

2r

D

`-2r`

Text Solution

Verified by Experts

Let `alpha, beta, gamma` be the roots of the given equation such that `alpha + beta = 0`. Then,
Sum of the roots = -p
`rArr" "alpha+beta+gamma = -p rArr gamma = -p`
But, `gamma` is a root of the given equation.
`therefore" "gamma^(3) + p gamma^(2) + q gamma + r = 0 rArr -p^(3) + p^(3) - pq + r = 0 rArr pq = r`
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