Finding Solutions

In the study of polynomial equations, it is important to understand how to find the solution of the equation. Equations of higher degree allow for

When a polynomial equation is set equal to 0, the solutions of the polynomial are the x-intercepts or roots of the corresponding graph. For example, to solve the equation, *x*^{4} *? x*^{3} ? 19*x*^{2} ? 11*x* + 31 = 0 graphically, means to find the roots or x-intercepts of the corresponding function, *f*(*x*) = *x*^{4} *? x*^{3} ? 19*x*^{2} ? 11*x* + 31. The graph below shows that there are 4 roots, at approximately *x* = -3, *x* = -2, *x *= 1, and *x* = 5. While these are not exact answers, they can be used to find exact answers using a table.