Question 30152: Question:
x^2+5x>24
Possible Answers:
a. none of these
b. -3
c. x<-3 or x>8
d. X<-8 or x>3
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! x^2+5x>24
That is x^2+5x-24 > 0
(x+8)(x-3) > 0
Since either positive multiplied by positive is positive OR
negative multiplied by negative is positive, there are two cases.
Case 1: Let (x+8) > 0 together with (x-3) > 0
This implies x > -8 together with x > 3
And since anything to the right of 3 is definitely to the right of (-8),
the verdict for this case is
x > 3
Case 2: Let (x+8) < 0 together with (x-3) < 0
This implies x < -8 together with x < 3
And since anything to the left of (-8) is definitely to the left of 3,
the verdict for this case is
x < -8
Therefore combining the results of both the cases we have
Answer: x< -8 and x > 3
Which is your choice (d)
Note: (factoring the quadratic expression: x^2+5x-24,
product =(-24) and sum is 5 and therefore the quantities are (+8) and (-5)
and therefore x^2+5x-24
= x^2+(8x-3x)-24
= (x^2+8x)-3x-24
=x(x+8)-3(x+8)
=xp-3p where p = (x+8)
=p(x-3)
=(x+8)(x-3)
|
|
|
