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Quadratic Inequalities

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 &#8211; 2) < 0 & ( 9x + 6 ) < 0 implies ( x &#8211; 2 ) ( 9x + 6 ) > 0 ------(2)

For &#8211;6/9 < x < 2 we get ( x &#8211; 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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SOLVE FOR 'X' 9X^2 - 12X - 12 > 0

QUESTION :- SOLVE FOR X

1. 9X^2 &#8211; 12X &#8211; 12 >0

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

9x^2 &#8211; 12x-12 > 0

= ...

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