Question

Solve the following inequality.

x^3+9x^2-108 less or equal to 0.
Then write your solution in interval notation. I am sooo confused and do not have any idea how to do this. Can someone please show me step by step please???

Thanks in advance. Someone who is confused.

Answer 1

This polynomial graphing might help sometimes:
http://mathportal.org/calculators/polynomials-solvers/polynomial-graphing-calculator.php

zeros at x = -6 (double zero) and x = +3
so we really have
(x+6)(x+6)(x-3)

It is negative for large negative x
it comes up and bounces off the x axis at x=-6, dropping down negative again
it does not actually come up and cross the x axis until x = 3
from then on it is positive,
therefore negative for
x</= +3 except for touching zero at x = -6