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Thread: Factorise a Quadratic Expression

  1. #1
    Junior Member
    Feb 2010

    Factorise a Quadratic Expression

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

    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:


    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
    Senior Member
    Jul 2010
    The above fact works only if the leading coefficient is 1. That is you must have an equation of the form $\displaystyle x^2+ cx+d$. But don't worry. You can do that just by dividing the 6 out. You get

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

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

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


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

    as required.
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