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algebra

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i have very little information in my math book on the following questions. can you either tell me the answer or a link where i can find my own answer. thanks

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?

  • algebra - ,

    1. b^2 < 4ac: 2 imaginary solutions.

    b^2 = 4ac: 1 real solution.

    b^2 > 4ac: 2 real soutions.


    2. Let's take a given Eq and solution
    sets and use the solutions to derive the Eq.

    Eq: y = 2x^2 + 5x + 2.

    Solution set: x = -1/2, and x = -2.

    x = -1/2,
    x + 1/2 = 0.

    x = -2,
    x + 2 = 0.

    (x + 1/2) (x + 2) = 0,
    Multiply the 2 binomials:
    x^2 + 2x + x/2 + 1 = 0,
    x^2 + 5x/2 + 1 = 0,
    Multiply both sides by 2 to eliminate the fraction and get:
    2x^2 + 5x + 2 = 0.

    The derived Eq is equivalent to the
    given Eq.

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