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I would like understanding if a quadratic will have one, two or no solution? How do I find a quadratic equation if I'm only given a solution. explain. an example of one or two solution to that creates a quadratic equation. having trouble downloading info. for review, any suggestions would be great.

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I would like understanding if a quadratic will have one, two or no solution? How do i find a quadratic equation if I'm only given a solution? Explain. An example of one or two solution to that creates a quadratic equation. having trouble downloading info. for review, any suggestions would be great.

Let us take a general quadratic equation:

Discriminant D =

If D < 0 then equation will have no real solutions.

If D = 0 then equation will have two equal solutions or you can say one solution depends on the terminology used in your class.

If D > 0 then equation will have two distinct solutions.

Let us take equation

Since D =
There will be NO real solutions.

Let us take equation

Since D =

It will have two equal solutions.

Let us take equation

Since D = >0
So there will be two distinct solutions.

It will have two equal solutions.

Now suppose we have solutions then we can find quadratic equation:

Let the solutions be 2 and 3

Then equation will be

x^2 - (sum of roots)x + product of roots = 0

x^2 - (2 + 3)x + 2*3 = 0

x^2 - 5x + 6 = 0

OR the other way is

(x -2)(x -3) = 0
x^2 - 5x + 6 = 0

Now suppose the equation has one solution 3, then equation will be

x^2 - (sum of roots)x + product of roots = 0

x^2 - (3 + 3)x + 3*3 = 0

x^2 - 6x + 9 = 0

OR the other way is (x - 3)(x - 3) =0
Equation will be

x^2 - 6x + 9 = 0

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