Algebra

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How do you find quadratic equations if you are only gven the solution?

  • Algebra -

    suppose you know the solutions are 5 and -3

    form factors (x-5) and (x+3), multiply them and set the result equal to zero

    (x-5)(x+3)=0
    x^2 -2x -15=0

  • Algebra -

    Is it possible to have diferent quadratic equations with the same solution? My instinct says yes, my fear of math says no.

  • Algebra -

    no
    any quadratic equation, which has been simplied to its simplest form has a unique solution, and given an set of solutions there is only one unique quadratic equation

    If I take the equation from my example and multiply it by 3 I would get
    3x^2 - 6x - 45 = 0

    it really is not a "different" equation.

    BTW, if your solutions had been fractions, say 4/5 and -2/3, your two factors would have been
    (5x-4) and (3x+2)

    There is another way:
    If you know the two solutions are m and n, then you can just form the quadratic by writing

    x^2 - (m+n)x + mn = 0, then simplify

    eg. going back to my example of solutions of 5 and -3, their sum is 2 and their product is -15

    the equation would be x^2 -(2)x + (15) = 0 , just like above

  • Algebra -

    change
    "the equation would be x^2 -(2)x + (15) = 0 , just like above" to

    the equation would be x^2 -(2)x + (-15) = 0 , just like above

  • Algebra -

    Wow! I have a lot to learn. I don't mean to take up your time, but I understand there is more than one way to solve quadratic equations. Is there a way you think is easier and how?

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