if `(1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8),` where `a,b,a_(0) ,a_(1)…….,a_(8) in R` such that `a_(0)+a_(1) +a_(2) ne 0` and
`|{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0` then the value of `5.(a)/(b) " is " "____"`

Answer

8

Explanation

Putting x=0, `a_(0) =1`
`(1+ax+bx^(2))^(4) =(1+ax+bx^(2))(1+ax+bx^(2))`
Clearly `a_(0)=1,a_(1) = " coefficients of " x=a+a+a+a=4a`
`a+(2)= " coefficients of " x^(2) =4b +6a^(2)`
`" Now " Delta =- (a_(0)^(3) +a_(1)^(3)+a_(2)^(3) =3a_(0)a_(1)a_(2))`
`:' a_(0)+a_(1)+a_(2)ne 0`
`:' a_(0)=a_(1) =a_(2)`
`1=4a =6a^(2)+4b`
`rArr a=(1)/(4),b=(5)/(32)`