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Math Help - Factorise a Quadratic Expression

  1. #1
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    Factorise a Quadratic Expression

    based on this text:
    How to Factorise a Quadratic Expression | eHow.com

    You factorise the quadratic expression x+ (a+b) x +ab by rewriting it as the product of two binomials (x+a) X (x+b). By letting (a+b)=c and (ab)=d, you can recognize the familiar form of the quadratic equation x+ cx+d. Factoring is the process of reverse multiplication and is the simplest way to solve quadratic equations.

    But I found an equation which has solutions and is not congruent with the above text, like:

    6x^2+5x-4=0

    Since the solution is: (2x-1)(3x+4)


    Based on the above text means, (a*b)=d --> (-1*4)= -4 ok but;
    (a+b)=c --> (-1+4)= 3 is not ok sine in the equation is 5.

    Please help me out... how this is possible etc.
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  2. #2
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    The above fact works only if the leading coefficient is 1. That is you must have an equation of the form x^2+ cx+d. But don't worry. You can do that just by dividing the 6 out. You get

    \displaystyle x^2+\frac{5}{6}x-\frac{4}{6} = 0

    from here \displaystyle a+b= \frac{5}{6} and \displaystyle ab =\frac{4}{6}

    \displaystyle-\frac{1}{2}\times\frac{4}{3} = -\frac{4}{6}

    and

    \displaystyle-\frac{1}{2}+\frac{4}{3} = -\frac{3}{6}+\frac{8}{6} = \frac{5}{6}

    as required.
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