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Product of roots of equation |(1+2x,1,1-...

Product of roots of equation `|(1+2x,1,1-x),(2-x,2+x,3+x),(x,1+x,1-x^2)|=0` is

A

`1//2`

B

`3//4`

C

`4//3`

D

`1//4`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `f(x)=|{:(1+2x,1,1-x),(2-x,2+x,3+x),(x,1-x,1-x^(2)):}|=0`
Constant term `=f(0)=|{:(1,1,1),(2,2,3),(0,1,1):}|=2+2-2-3=-1`
Also coefficient of `x^(4)` is `'-2'`
Hence product of roots is `1//2`.
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