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If |{:(1+x^(2),3x,x+1),(5,x,x^(3)),(0,1,...

If `|{:(1+x^(2),3x,x+1),(5,x,x^(3)),(0,1,x+2):}|=(alpha_(1)-x)(alpha_(2)-x)(alpha_(3)-x)(alpha_(4)-x)(alpha_(5)-x)` is an identity, where `alpha_(1),alpha_(2),alpha_(3),alpha_(4),alpha_(5)` are complex numbers independent of `x` ,then the value of ` alpha_(1)*alpha_(2)*alpha_(3)*alpha_(4)*alpha_(5)` is

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