Do you agree that a quadratic equation has at most two solution? justify your answer and give example.

Quadratic equation can have one or two solutions. It depends on the value of diferentiator of this equation. If this value is positive, there are two solutions from the real field of numbers. If the value is equal zero, there is one doubled solution (from complex or real field). Finally, when this value is negative, there are two solutions from complex field. 
Examples:

x2-2x+1=0 the value of diferentiator of this equation equals 0, so there is one doubled solution: x=1.
x2-3x+2=0 the value of diferentiator of this equation is positive, so there are two real solutions: x=-1, x=-2.

Where’s the graph too show me?