If `sin^(2)alpha,cos^(2)alphaand-cosec^(2)alpha` are the zeros of `P(x)=x^(3)+x^(2)+ax+b(a,binR)`. Then P(2) equals ______.

Answer

9

Explanation

We have `x^(3)+x^(2)+ax+b=0`
Sum of roots =-1
`implies1-cosec^(2)alpha=-1`
`impliessin^(2)alpha=(1)/(2)`
Thus, `cos^(2)alpha=(1)/(2)`
So, `P(x)=(x-(1)/(2)).(x-(1)/(2))(x+2)`
Hence, `P(2)=(3)/(2).(3)/(2).4=9`