$a)$

$x^4-6x^3+5x^2=0$

$x^2\left(x^2-6x+5\right)=0$

$x^2=0\vee x^2-6x+5=0$

$x=0\vee \Delta ={\left(-6\right)}^2-4\cdot 1\cdot 5=36-20=16$

$\sqrt{\Delta }=4$

$x_1=\frac{6-4}{2}=\frac{2}{2}=1$

$x_2=\frac{6+4}{2}=\frac{10}{2}=5$

$x\in \left\{0,1,5\right\}$