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Let alpha, beta and gamma are the roots ...

Let `alpha, beta and gamma` are the roots of equation `x^(3) + ax^(2) + bx + c = 0 (a, b, c in R, a != 0)`. If system of equations
`alphax + betay + gammaz = 0`
`betax + gammay + alphaz = 0`
`gammax + alphay + betaz = 0`
has non trivial solution then the value of`((a^2)/(b))` is :

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`|(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=0`
`implies alpha^(3)+beta^(3)+gamma^(3)-3alpha beta gamma = 0`
`implies alpha = beta = gamma`
Now `3 alpha = -a` `3alpha^(2) = -b`
Hence `(a^2)/(b) = 3`.
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