lean_workbook_plus_34910

Prove that for a real number $t$, we have $f(t)=0$ or $f(t)=t^2$. Also, prove that if $f(\alpha)=0$ for a $\alpha\neq 0$, then $f(x)\equiv 0$. If $f(x)\neq 0$ for all $x\neq 0$, then prove that $f(x)\equiv x^2$.