SOLUTION: please help me to answer this in simple terms so I can understand. Why are there usually two solutions in quadratic equations? Thank you!

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Question 382916: please help me to answer this in simple terms so I can understand.
Why are there usually two solutions in quadratic equations?

Thank you!
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
If you solve ax^2+bz+x = 0
you will get:
x = [-b +- sqrt(b^2-4ac)]/(2a)
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You get two solutions because of the +-
in the quadratic formula.
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x = [-b + sqrt(b^2-4ac)]/(2a) and x = [-b - sqrt(b^2-4ac)]/(2a)
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Cheers,
Stan H.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
There are always 2 solutions to a quadratic equation, not just usually.
Sometimes it's the same solution 2 times, called a "multiplicity of 2."
eg, has solutions of x = -2 and x = -2.
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Cubic equations (3rd order) always have 3 solutions.
4th power, quartics, always have 4, etc.
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As to the why of this, it's because there are always 2 values that will satisfy a quadratic.