Question

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Answer 1

Some polynomial equations have complex solutions.

Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.

Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.

Answer 2

Let's put it this way:  If you plot a few non-x-intercept points and then draw a curvy line through them,you will not know if you got the x-intercepts even close to being correct. The only way you can be sure of your x-intercepts is to set the quadratic equal to zero and solve. So its a matter of guessing from the pictures. Basicaly said, the calculator won't give you the exact result.