Solving Polynomial Equations

Let's first graph the two functions. $$\begin{array}{r}y=2x^4-5x^3-3x^2\text{and}y=0\end{array}$$ We can enter these into a graphing calculator by pushing $\boxed{\text{Y}=}$ and typing the right-hand side in the first two rows.

By pushing $\boxed{\text{GRAPH}},$ the calculator will draw the equations. For those functions and their intersections to be visible on the screen, re-size the standard window by pushing the $\boxed{\text{WINDOW}}$ button. Change the settings to a more appropriate size and then push $\boxed{\text{GRAPH}}.$

We see that the graphs intersect three times, so there are three solutions to this equation. To determine them, use the intersect option by pressing $\boxed{2\text{ND}}$ and then $\boxed{\text{CALC}}.$

Next, to help the calculator work faster, we will have to provide it with some guess as to where the intersections occur. To make sure the calculator picks the intersection point we want to find, make our guess as close as possible to it. We have to repeat this procedure for all three solutions.

The three solutions are $x=\text{-}0.5,$ $x=0,$ and $x=3.$