For finding the type of solution,we use the discriminant(D)

If
D>0,solutions are real and unequal
D=0,solutions are real and equal
D<0,solutions are imaginary

In quadratic of form [ax^2+bx+c=0]
the sum of roots is given by
(-b/a)
the product of the roots is given by
(c/a)

The number of roots will always be 2,never more,never less. Obviously we need to know ABC to calculate the roots. And A can never be equal to zero,as this would make the quadratic void.

Hope this helps,
-Prabhat