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jatt-rockz November 5th, 2011 07:31 PM

Inequality
 
Solve each inequality graphically. State the solution and graph the solution:
a) (X^3) (6x^2) +5x+12 >0
b) X/(x^2 -2x-8) >0

Zahar November 5th, 2011 08:08 PM

Re: Inequality
 
1 Attachment(s)
I do not know right answer but in my head))) exist this:
X/(x^2 -2x-8) >0
for the (x^2 -2x-8) :
x = [ 2 +/- square_root( 2^2 - 4*(-8) ) ] / 2 = 1 +/- square_root( 4 + 32 )/2 =
= 1 +/- 6/2 = 1 +/- 3 = { 4, -2 } (x1 = 4 and x2 = -2)

then we can to write
x/(x^2 -2x-8) = x / [ (x - x1)*(x - x2) ] = x / [ (x - 4)*(x + 2) ]

I think this
x do not equal 4 and -2 because we will have division by zero (but we used this numbers to transform equation)

we have x from ( - infinity) to (+ infinity)
then

case ( x < - 2 ) : (-) /[ (-)*(-) ] < 0 /* because x < 0, x - 4 < 0 , x + 2 < 0 as conclusion from that :: x < - 2 */

case ( -2 < x < 0 ) : (-) /[ (-)*(+) ] > 0 /* because x < 0, x - 4 < 0 , x + 2 > 0 as conclusion from that :: -2 < x < 0 */

case ( 0 < x < 4 ) : (+) /[ (-)*(+) ] < 0 /* because x > 0, x - 4 < 0 , x + 2 > 0 as conclusion from that :: 0 < x < 4 */

case ( 4 < x ) : (+) /[ (+)*(+) ] > 0 /* because x > 0, x - 4 > 0 , x + 2 > 0 as conclusion from that :: 4 < x */

But ! You need to write it in proper form, which is demanded by teacher, book, because I do not know the rules of ...

soroban November 5th, 2011 08:21 PM

Re: Inequality
 
Hello, jatt-rockz!

Quote:

Solve each inequality graphically.
State the solution and graph the solution:

[color=beige]. . [/color]



[color=beige]. . [/color]When is it positive?
[color=beige]. . [/color]When is its graph above the x-axis?

The function factors:[color=beige] .[/color]
[color=beige]. . [/color]Its x-intercepts are:[color=beige] .[/color]

The graph looks like this:

Code:

            |
            |                  *
            |
            | *                *
      -1 * |    *          *
  - - - o - + - - - o - - - o - - -
      *    |      3  *  4
            |
      *    |
            |










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