# Richard Perito's question at Yahoo! Answers regarding finding a quadratic having the given roots

#### MarkFL

##### Administrator
Staff member
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

##### Administrator
Staff member
Hello Richard Perito,

I would begin by writing the roots as:

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

And so from the quadratic formula:

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

we see we have:

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

Hence, the quadratic:

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

has the given roots.