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Let |(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),...

Let `|(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x)|=1/6(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4))` be an indentity in `x`, where `alpha_(1),alpha_(2),alpha_(3),alpha_(4)` are independent of `x`. Then find the value of `alpha_(1)alpha_(2)alpha_(3)alpha_(4)`.

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Verified by Experts

The correct Answer is:
6
Since it is an identity the value of L.H.S and R.H.S are equal for all values of `x`
put `x=0impliesalpha_(1)alpha_(2)alpha_(3)alpha_(4)=6`
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