If `x^2-1` is `a` factor of `a x^4+b x^3+c x^2+dx+e ,` show that `a+c+e=b+d`
Given ,`x^2−1` is a factor of `ax^4+bx^3+cx^2+dx+e`
`(x−1)(x+1)` divides `ax^4+bx^3+cx^2+dx+e`
`When,x=1,a+b+c+d+e=0 (i)`
`When ,x=−1, then a−b+c−d+e=0`(ii
`a+c+e=b+d`

Explanation

If `x^2-1`
is `a`
factor of `a x^4+b x^3+c x^2+dx+e ,`
show that
`a+c+e=b+d`
Given ,`x^2−1` is a factor of `ax^4+bx^3+cx^2+dx+e`

`(x−1)(x+1)` divides `ax^4+bx^3+cx^2+dx+e`
`When,x=1,a+b+c+d+e=0 (i)`
`When ,x=−1, then a−b+c−d+e=0`(ii)
`a+c+e=b+d`