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    Quadratic equations

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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.

    © BrainMass Inc. brainmass.com December 24, 2021, 8:29 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/quadratic-equations-solution-280923

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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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:29 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/quadratic-equations-solution-280923

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