Learning Resources

Focus D: Roots of Polynomial Equations

Step F

A quartic equation has four roots. If 4 - i is a root, then 4 + i is also a root. Similarly, if -1 + 2i is a root, then -1 - 2i is a root as well. The quartic equation with roots 4 i and -1 2i can be determined by the following procedure.

• Obtain a quadratic equation by finding the sum and product of the two roots 4 + i and 4 - i.
• Obtain another quadratic equation by finding the sum and product of the two roots -1 + 2i and -1 -2i.
• Multiply the two resulting quadratic equations together to produce the desired quartic equation.