Question 379391
All quadratics have two solutions in the complex plane (including multiplicities). However, you can determine how many (real) solutions a quadratic has by looking at the discriminant (b^2 - 4ac). If the discriminant is positive, the quadratic has two real solutions; if it is zero, the quadratic has one double root, and if it is negative, the quadratic has two complex roots.

Also, a quadratic is uniquely determined by its roots. A quadratic with roots r_1 and r_2 must be in the form (x - r_1)(x - r_2) = 0, or x^2 - (r_1 + r_2)x + r_1r_2 = 0.