If you have the equation

x^2 + 2x - 3 = 0 You can factor the quadratic to get

(x - 1)(x + 3) = 0 and hence the roots

x = 1 and x = -3

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 are complex,

for example suppose that the roots are

5 + 3i and 5 - 3i then the quadratic equation is

(x - 5 - 3i)(x - 5 + 3i) = 0

which simplifies to

x^2 - 10x + 34 = 0

Cheers,

Adarsh