If `x=0` and `x=-1` are the roots of the polynomial `f(x)=2x^3-3x^2+a x+b ,` find the value of `a` and `b`

Explanation

Given: `x=0` and `x=-1`
`f(x)=2x^3-3x^2+ax+b`
Putting `x=0` in `f(x)`, we get
`f(0)=2(0)^3-3(0)^2+a(0)+b`
`b=0`
Putting `x=-1` and `b=0` in `f(x)`, we get
`f(-1)=2(-1)^3-3(-1)^2+a(-1)+0`
`0=-2-3-a`
`a=-5`
Hence, the value of `a=-5` and `b=0`.