Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 8, -i, i?

Answer 1

`x^3-8x^2+x-6`

Explanation:

The polynomial with zeros `x_1, x_2 and x_3` is

`x^3-(x_1+x_2+x_3)x^2+(x_2x_3+x_3x_1+x_1x_2)x-x_1x_2x_3`

Here, it is

`x^3-(8+i-i)x^2+(-i^2-8i+8i)x-(9)(i)(-i)`

`=x^3-8x^2+x-6`