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The determinant Delta=|{:(a,b,aalpha+c),...

The determinant `Delta=|{:(a,b,aalpha+c),(b,c,balpha+c),(aalpha+b,balpha+c,0):}|` is equal to zero if

A

a,b,c are in A.P.

B

a,b,c are in H.P

C

`x-alpha` is a factor of `ax^(2)+2bx+c`

D

`x-alpha` is a factor of `ax^(2)+bx+c`

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The correct Answer is:
C
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