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If alpha,beta,gamma are the roots of p x...

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

A

p

B

q

C

0

D

r

Text Solution

Verified by Experts

The correct Answer is:
C
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
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