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

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Answer 1 · 2015-06-04T20:36:20

I'll try doing it without the GC:

You may have noticed that the function can be rewritten:

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

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

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

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

How do I use a graphing calculator to find the complex zeros of f(x)=x3−4x2+25x−100f(x)=x^3-4x^2+25x-100?