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.

The additional roots are: and

Step-by-step explanation:

Given

Roots: and

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:

The conjugate of is: .

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

The conjugate of is and the conjugate of is

Hence, the additional roots are: and

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