Question 62826
QUESTION:


(x+8)(x-2)<0

ANSWER:

(x+8)(x-2)<0

Remove the brackets by multiplying term by term,

x*x - x*2 + 8* x - 8*2 < 0

x^2- 2x + 8x -16 < 0

x^2 + 6x -16 < 0

We can solve this equation using quadratic formula,



{{{x  <  (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


Here  a = 1  b = 6 and c = -16


{{{x  <  (-6 +- sqrt( 6^2-4*1*-16))/(2*1) }}}


 {{{x  <  (-6 +- sqrt( 36+64 ))/(2) }}}  


{{{x  <  (-6 +- sqrt( 100))/(2) }}} 


{{{x  <  (-6 +- 10)/(2) }}} 

==> x <  (-6 + 10)/2    or  

    
    x < ( -6 - 10 )/ 2



==> x < 4 /2    or   
 

    x < -16/2




==> x < 2    or  


    x < -8


This the required solutions.



Regards.

praseenakos@yahoo.co.in