# algebra II

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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. Provide your
classmateâ€™s with one or two solutions with which they must create a quadratic equation.

• algebra II -

So what is your thinking? We will be happy to critique your thinking.

• algebra II -

Usually a quadratic equation will be squared but it depends on the power of x.
b^2 - 4ac (the discrimant) determines number of solutions.
if > 0, 2 solutions
if = 0, 1 solution (a double solution)
if < 0, 0 (real) solutions (but 2 imaginary)

Given solutions x = 2, x = -4; equation is:
(x-2)(x+4) = 0 or x^2 + 2x - 8 = 0

Different equations only in the sense they are a multiple of the original one. x^2 + 3x + 5 = 0 and
2x^2 + 6x + 10 = 0 are multiples of each onther and have the same solutions.

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