1. ## [SOLVED] Proving?

If $(x - a)^2$ is a factor of $x^3 + mx^2 + n$, prove that $27n + 4m^3 = 0$

2. Let $f(x)=x^3+mx^2+n$

If $(x-a)^2$ is a factor of f, then $f(a)=0, \ f'(a)=0$

$f(a)=0\Rightarrow a^3+ma^2+n=0$

$f'(a)=0\Rightarrow 3a^2+2am=0\Rightarrow a(3a+2m)=0$

If $a\neq 0\Rightarrow a=-\frac{2m}{3}$

Now replace a in $f(a)=0$

3. Lol Thanks. I nearly found it but my a was $\frac{-2}{3}$. Thanks for clearing it up for me.