Learning Resources

Focus D: Roots of Polynomial Equations

Step C

A quartic equation has four roots. If two of the roots are 7i and -3i, then the other two roots are -7i and 3i. The quartic equation with roots 7i and 3i can be determined by the following procedure.

• Obtain a quadratic equation by finding the sum and product of the two roots 7i and -7i.
• Obtain another quadratic equation by finding the sum and product of the two roots 3i and -3i.
• Multiply the two resulting quadratic equations together to produce the desired quartic equation.