Find the value of `a` and `b` so that the polynomial `x^3-a x^2-13 x+b` has `(x-1)` and `(x+3)` as factors.

Explanation

Let `f(x)=x^3−ax^2−13x+b`
`(x−1)` and `(x+3)` are factors of `f(x)`
According to the factor theorem, if `(x−a)` is a factor of `f(x)`, then `f(a)=0`
`therefore f(1)=0` and `f(−3)=0`
`⇒f(1)=1−a−13+b=0`
`⇒b−a=12` ....(i)
And,
`⇒f(−3)=−27−9a+39+b=0`
`⇒b−9a=12`
`∴ b=12+9a`
Substituting the value of `b` in equation (i), we get:
`=>12+9a−a=12`
`⇒8a=0`
`=>a=0`
`=>b=12+9a`
`=>b=12+9(0)`
`=>b=12`
`therefore` The value of `a=0` and `b=12`