Question 173956
How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. 
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A quadratic will always have 2 solutions.
However, sometimes the 2 solutions are the same.  For example:
x^2 -2x + 1 = 0
(x-1)*(x-1) = 0
x = 1
x = 1
It's the same point, (1,0), so some will say it's one solution.  You can get into semantics.
Also, sometimes the solutions will be complex numbers, instead of real.
For example:
x^2 + 4 = 0
*[invoke solve_quadratic_equation 1,0,4]
This has no REAL number solutions, but still has 2 solutions.  You can see it doesn't cross the x-axis.
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There are an infinite number of quadratics with the same 2 solutions.  2 points don't define a parabola (to put in graphic terms), 3 are required to define the curve AFTER it's defined to be a parabola.