Subject: Find a Quadratic Equation given roots
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