If $f \in D[x]$ has $f` a=0=f` b$ for $a \neq b$ in $D$, show that $f$ is divisible by $(x-a)(x-b)$
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]