What are the zeros of
Step 1 Use a graphing calculator to find any real roots. The graph of
Does the graph show all of the real roots?
Yes; the graphs of quartic functions have one or three turning points. Since the graph shows three turning points, it will not turn again to cross the x-axis a third time.
Step 2 Factor out the linear factors
Step 3 Use the Quadratic Formula. Find the complex roots of
The complex roots are
Step 4 The four zeros of the function are
By the Fundamental Theorem of Algebra, there can be no other zeros.
Reasoning The graph of