How do I use a graphing calculator to find the roots of the polynomial equation #x^3-4x^2+x+26=0#?

1 Answer
Sep 13, 2014

To find the roots of #x^3−4x^2+x+26=0#, I graphed the equation:
my screenshot

I used a feature called "Analyze" graph to find (-2,0) as the solution.
That is the only real solution to the problem. In order to find the remaining two imaginary/complex solutions, you should perform either long division or synthetic division.

I also used the CAS feature of my calculator to get me the resulting factor: #x^2-6x+13#. Solving this quadratic with the quadratic equation yields: #frac{6+sqrt(36-52)}{2}=frac{6+sqrt(-16)}{2}# which simplifies to #3+-2i# .