Learning Resources

Focus D: Roots of Polynomial Equations

Step E

Note that one of the given roots is real. The question refers to a cubic equation, and all polynomial equations of odd degree have at least one real root. The other given root is 2i. Thus, -2i is also a root. The cubic equation with roots 2i and
 -11 can be determined by the following procedure.

• Obtain a quadratic equation by finding the sum and product of the two roots 2i and -2i.
• Since -11 is a root, (x + 11) must be a factor of the cubic equation.
• Thus, multiply the resulting quadratic equation by the expression (x + 11).