When you solve a word problem involving a quadratic equation which of the following is not a number of solutions can you possibly get?
0
1
2
3

It depends on the value of the discriminant of the quadratic.  

If you are familiar with the quadratic formula...

x=(-b±√(b^2-4ac))/(2a)

The part under the radical sign (b^2-4ac) is called the discriminant of the quadratic  (of the form ax^2+bx+c)

If the discriminant is less than zero there are no REAL solutions  (however there are two imaginary solutions)

If the discriminant is equal to zero, there is just one solution

If the discriminant is greater than zero, there are two real solutions.

So depending on context, if you are to exclude imaginary solutions (which we often do) you can have 0,1, or 2 real solutions.

However you will NEVER have three solutions. (real or imaginary)