Question

Find the values of x which satisfy the following inequation:
x3 – x² <12x​

Answer 1

x< -3 and 0 < x < 4

Explanation:

x^3 – x² <12x​

Subtract 12x from each side

x^3 -x^2 - 12x< 0

Factor

x( x^2 -x-12) <0

Factor

x( x-4) ( x+3) < 0

Using the zero product property

x=0 x=4 x=-3

We have to check the signs regions

x < -3

-( -) (-) < 0 True

-3 to 0

-( -) (+) < 0 False

0 to 4

+( -) (+) < 0 True

x>4

+( +) (+) < 0 False

The regions this is valid is

x< -3 and 0 < x < 4