Answer
$\{0,0,3\pm\sqrt 2 \}$
Work Step by Step
Step 1. Factor the polynomial $f(x)=x^2(x^2-6x+7)$
Step 2. For $x^2=0$, we have $x=0$ (multiplicity 2)
Step 3. For $x^2-6x+7=0$, we have $x=\frac{6\pm\sqrt {6^2-4(7)}}{2}=3\pm\sqrt 2$
Step 4. The zeros are $\{0,0,3\pm\sqrt 2 \}$
