Chapter 5 - Section 5.7 - Polynomial Equations and Their Applications - Exercise Set - Page 390: 43

$0,2$

Given: $x^4-4x^3+4x^2=0$ or, $x^2(x^2-4x+4)=0$ Need to use factorization to solve the quadratic equation. This can be factorized as follows: $x^2(x-2)^2=0$ Set each factor equal to zero, we get Now, $x^2=0 \implies x=0$ and $x-2=0$ Thus, $x=0,2$