Find the solution set of each of the following quadratic inequalities x squared + 9x + 14 > 0

1
by jrt

2015-09-12T18:47:40+08:00
First, make the inequality an equation (just change the greater than sign to equal sign)

second, solve for the value of x using any method (it would be much easier if you would use factoring, so i used factoring technique)

x squared + 9x + 14 = 0
(x + 7) (x + 2) = 0
x + 7 = 0                 x + 2 = 0
x = 0-7                    x = 0-2
x = -7                      x = -2

(-7) squared + 9(-7) + 14 = 0          (-2) squared + 9(-2) + 14 = 0
49 - 63 + 14 = 0                            4 - 18 + 14 = 0
-14 + 14 > 0 FALSE                     -14 + 14 > 0 FALSE

try -8 or -1 as the solution

(-8) squared + 9(-8) + 14 = 0    (-1) squared + 9(-1) + 14
64 -72 + 14 = 0                        1 - 9 + 14 = 0
-8 + 14 > 0                               -8 + 14 = 0
6 > 0 TRUE                             6 > 0 TRUE

it means that the solution set are the numbers lesser than -7 like -8 up to negative infinity and greater than -2 like -1 up to positive infinity

{ x | x -7>x>-2 }
or
{ x | x < -7 or x > -2 }

(x | x means for all the values of x such that x is lesser than -7 but greater than -2)

note: -7 and -2 are not included at the solution set since the sign is not greater than or equal to, it is included if it is signed like greater than or equal to.

hope i helped u.. :)

~Roiete