Given the equation , find an equation whose roots are each less than the roots of the given equation.

Source: NCTM Mathematics Teacher, August 2006

**Solution**

If we graph the given equation as a function , we see that it has one real root at . The other two roots are complex and not shown. To get a new equation that has also three roots each less than the roots of the given equation, all we have to do is shift the graph to the left by units. Algebraically, it means replacing by

**Answer**: