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Consider the system of equations : x...

Consider the system of equations :
`x+y+z=0`
`alpha x+beta y+gamma z=0`
`alpha^(2)x+beta^(2)+gamma^(2)z=0`
Then the system of equations has

A

a unique solution for all values of `alpha, beta, gamma`

B

infinite number of solutions if any two of `alpha, beta, gamma` are equal

C

a unique solution if `alpha, beta, gamma` are distinct

D

more than one, but finite number of solution depending on values of `alpha, beta, gamma`

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