The easy way to tell the nature and number of roots of a quadratic equation is by evaluating its discriminate. The discriminate of a quadratic equation in the form ax^2 + bx + c = 0 is b^2 - 4ac.
If b^2 - 4ac = 0 there is 1 real root
If b^2 - 4ac > 0 there are 2 distinct real roots
If b^2 - 4ac < 0 there are 2 imaginary roots.