Question

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

Answer 1

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

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` .