Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.
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The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+i is a root, so 6-i is also a root.
So the simplest polynomial you can build with these roots is
(x - (-5)) (x - (6 + i )) (x - (6 - i )) = x ^3 - 7x ^2 - 23x + 185
(first choice)