Yes, I agree that Quadratic Equation has two roots. It's justified by its meaning. Quadratic Equation is an equation of the second degree in its variable or variables. As a student also, I remember that you determine the number of roots by its degree. It can be solve by Factoring or using Quadratic formula.
Ex. By factoring
since, x^2-x-6= (x-3)(x+2)
Setting each linear factor to zero, we get
Hence the roots are,
x=3 and x=-2