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Thread: produce of eq with sor and por

  1. #1
    Junior Member
    Jul 2008

    produce of eq with sor and por

    roots a/b, 1/ab

    sor = a/b + 1/ab
    = (a^2+1 )/ab

    por = a/b X 1/ab
    = a/ab^2

    form the eq with details pls.

    (answer provided is abx^2 -a^2x +1 = 0)
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  2. #2
    MHF Contributor Matt Westwood's Avatar
    Jul 2008
    Reading, UK
    I presume "sor" means "sum of roots" and "por" means "product of roots".

    From that, I also presume that you are to create a quadratic equation which has roots as given.

    Let $\displaystyle ax^2 + bx + c$ be a quadratic equation.

    The sum of roots is $\displaystyle -b/a$ and the product of roots is $\displaystyle c/a$.

    (This can be proved from forming the product and sum of the roots as given by the quadratic formula $\displaystyle x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}$ and simplifying the expression you get.)

    So this gives you $\displaystyle x^2 - \left({\frac {a}{b} + \frac {1}{ab}}\right) + \frac {1}{b^2}$

    But if you simplify this equation, you don't get what you've given as the answer.

    If you try and solve what your answer provides using the quadratic formula you get:

    $\displaystyle x = \frac {a^2 \pm \sqrt {\left({a^2}\right)^2 - 4ab}} {2ab}$

    and that's nowhere near an equation giving the above as roots.

    So there's either something wrong with the question or it's been copied down wrong.
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