If $x^2-3x+2$ is a factor of $x^4-a{x}^2+b=0$ then the equation whose roots are a and b is

$x^4-a{x}^2+b=\left(x^2-3x+2\right)p\left(x\right)$

$=(x-1)(x-2)p\left(x\right)$

where $p\left(x\right)$ is a polynomial of degree 2

$\therefore 1-a+b=0$ and $16-4a+b=0$

$\Rightarrow a=5,b=4$

Thus, equation whose roots are a and b is

$x^2-9x+20=0$