Form a​ third-degree polynomial function with real​ coefficients, with leading coefficient​ 1, such that 8 plus i and 7 are zeros.

Answer 1

To get real coefficients, complex roots must be in pairs. This means that the third root is 8 - i

So

f(x) = (x-7) ( x - [8 + i] ) ( x - [8 - i] )

Multiplying all this out gives

f(x) = x³ - 23 x² + 177 x -455