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    Quadratic Inequalities

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    SOLVE FOR 'X' 9X^2 - 12X - 12 > 0

    QUESTION :- SOLVE FOR X

    1. 9X^2 -12X -12 >0

    SOLUTION: The above given inequality is an quadratic which has two factors

    9x^2 -12x-12 > 0

    = 9x^2 –18x + 16x –12 > 0

    = 9x(x-2) + 6(x-2) > 0

    = (x -2) (9x + 6)>0

    which implies the product of (x -2) & (9x + 6 ) > 0
    Therefore two factors has to be +tive (or) –tive values
    For x >2 we have ( x- 2) > 0 & ( 9x + 6 ) > 0 implies ( x -2 ) ( 9x + 6 ) > 0 ----------(1)

    For x < - 6/9 we have ( x -2) < 0 & ( 9x + 6 ) < 0 implies ( x -2 ) ( 9x + 6 ) > 0 ------(2)

    For &#8211;6/9 < x < 2 we get ( x -2 ) ( 9x + 6 ) < 0 -----(3)

    From ( 1) (2) (3) we infer that &#8216;x&#8217; belongs to [ ( -&#940;,- 6/9) U ( 2, &#940;) ] HENCE THE SOLUTION FOR &#8216;X&#8217;

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    https://brainmass.com/math/basic-algebra/quadratic-inequalities-31705

    Solution Preview

    SOLVE FOR 'X' 9X^2 - 12X - 12 > 0

    QUESTION :- SOLVE FOR X

    1. 9X^2 -12X -12 >0

    SOLUTION: The above given inequality is an quadratic which has two factors

    9x^2 -12x-12 > 0

    = 9x^2 ...

    Solution Summary

    Quadratic inequalities are examined.

    $2.49

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