Question

If $0$ and $1$ are the zeros of the polynomial $f\left(x\right)=2x^3-3x^2+ax+b$, find the value of a and b

Answer 1

Given,

$f\left(x\right)=2x^3-3x^2+ax+b$

Roots $x=0,1$

$f\left(0\right)=0\Rightarrow 2(0{)}^3-3(0{)}^2+a\left(0\right)+b=0\Rightarrow b=0$

$f\left(1\right)=0\Rightarrow 2(1{)}^3-3(1{)}^2+a\left(1\right)+0=0\Rightarrow -1+a=0\Rightarrow a=1$

$\therefore a=1,b=0$