Subject: Find a Quadratic Equation given roots

Name: MC
Who is asking: Student
Level: Secondary

Question:
How do I find the equation for the quadratic with roots at 2-i and its complex conjugate?

If you have the equation

You can factor the quadratic to get

and hence the roots

Conversely, if you have the roots x = 1 and x = -3 you can recover the quadratic equation by forming (x - 1)(x + 3) = 0.

The same is true if the roots ate complex, for example suppose that the roots are 5 + 3i and 5 - 3i then the quadratic equation is

which simplifies to