If `alpha,beta,gamma` are the roots of `p x^3+q x^2+r=0,` then the value of the determinant `|(alphabeta,betagamma,gammaalpha),(betagamma,gammaalpha,alphabeta),(gammaalpha,alphabeta,betagamma)|` is `p` b. `q` c. `0` d. `r`

Options

A. p
B. q
C. 0
D. r

Answer

C

Explanation

Operating `C_(1) to C_(1) +C_(2) +C_(3)` gives
`(alpha beta+ beta gamma+gammaalpha) |{:(1,,betagamma,,gammaalpha),(1,,gammaalpha,,alphabeta),(1,,alphabeta,,betagamma):}|`
from the given equation `alpha beta +beta gamma +gamma alpha =0` so the value of determinant is 0