[SOLVED] Proving?

**mark1950** · June 5th 2009, 08:53 PM

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

**red_dog** · June 5th 2009, 09:11 PM

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 $f(a)=0$

**mark1950** · June 5th 2009, 09:30 PM

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

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