Question 1803: Why are there usually two solutions in quadratic equations
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! a quadratic is any equation of the form  , where a, b, c are constants.
The largest power is  . This ALWAYS gives a "u" or a "n" shaped graph. So, these shapes will cross the x-axis either 2 times, or perhaps just once or perhaps never...but NEVER more than 2 times.
Where the curve (equation) crosses the x-axis, these are the ROOTS, because here, we are saying at this/these point(s), y=0...what are the x-values.
Similarly, a straight line will cross the x-axis just once (or possibly never), but never more than once, so any straight line will have (usually) just 1 root..1 "answer".
cheers
Jon.
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