# How do I use a graphing calculator to find the complex zeros of f(x)=x^3-4x^2+25x-100?

Jun 4, 2015

I'll try doing it without the GC:

You may have noticed that the function can be rewritten:

$f \left(x\right) = {x}^{2} \left(x - 4\right) + 25 \left(x - 4\right) \to$
$f \left(x\right) = \left({x}^{2} + 25\right) \left(x - 4\right) \to$

If $f \left(x\right) = 0$ then the only real root is $x = 4$

And the complex roots come from
${x}^{2} = - 25 \to x = 5 i \mathmr{and} x = - 5 i$

Btw I have no idea how to do this with a GC.