Question 264621: 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? Please explain and provide examples if possible.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you know if a quadratic equation will have one, two, or no solutions?
Use the discriminant: b^2-4ac
If <0, 2 complex solutions; y = x^2-2x+9
If =0, 2 equal Real solutions: y = x^2 + 2x + 1
If >0, 2 unequal Real solutions: y = x^2 -2x -9
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How do you find a quadratic equation if you are only given the solution?
If the solutions are "a" and "b"
the equations is
y = (x-a)(x-b)
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Is it possible to have different quadratic equations with the same solution? Please explain and provide examples if possible.
Yes
y = (x-2)(x+3)
y = -(x-2)(x+3)
Solutions are 2 and -3. One parabola opens up; the other opens down.
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Cheers,
Stan H.
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