Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3+i, 3-i?

Answer 1

`x^2-6x+10`

Explanation:

If the roots are `x_1 and x_2`, the quadratic is

`x^2-((x_1+x_2)x+x_1x_2`.

Here, it is

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

`=x^2-6x+(3^2-(i)^2)`

`=x^2-6x+10`