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 identity 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)`

Answer

6

Explanation

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