MHB Richard Perito: Find Quadratic with Roots -1 +/- i√2

[MarkFL]

Here is the question:

Write a quadratic equation with the solution set -1 + i√2, -1 - i√2?

I have posted a link there to this topic so the OP can see my work.

 

[MarkFL]

Hello Richard Perito,

I would begin by writing the roots as:

$$x=-1\pm i\sqrt{2}=\frac{-2\pm\sqrt{-8}}{2}$$

And so from the quadratic formula:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

we see we have:

$$a=1,\,b=2,\,b^2-4ac=4-4c=-8\implies c=3$$

Hence, the quadratic:

$$f(x)=x^2+2x+3$$

has the given roots.