Question

A polynomial equation with rational coefficients has roots +5 plus 12 i and −−negative 9 minus 7 i. List two more roots of the equation.

Answer 1

The additional roots are:
`5 - 12i` and
`-9 + 7i`

Explanation:

Given

Roots:
`5 + 12i` and
`-9 -7i`

Required

Determine two additional roots

For a polynomial with two rational roots, the additional roots are the conjugates of the roots.

Take for instance, the following expression:

`a + \sqrt b`

The conjugate of
`a + \sqrt b` is:
`a - \sqrt b`.

Having established how to determine the additional roots, we proceed to determine the roots.

The conjugate of
`5 + 12i` is
`5 - 12i` and the conjugate of
`-9 -7i` is
`-9 + 7i`

Hence, the additional roots are:
`5 - 12i` and
`-9 + 7i`