solve each polynomial inequality. Approximately to three decimal places if necessary?
(x + 4)(3x - 9) (x - 1) < 0
- llafferLv 71 month ago
Since this is already factored makes this easier. If this were an equation we'd see that the roots are:
x = -4, 1, 3
(3x - 9) can be factored further to 3(x - 3), then dividing both sides by 3 would get rid of the 3.
We can use this information to check values between the roots and see which ones result in a value less than zero (aka, negative numbers):
if x > 3 we have positive times positive times positive, which is positive.
if 1 < x < 3 we have positive times positive times negative, which is negative.
if -4 < x < 1 we have positive times negative times negative, which is positive.
if x < -4 we have negative times negative times negative, which is negative.
So the solution to your inequality is:
x < -4 and 1 < x < 3
(-∞, -4) U (1, 3)