SOLUTION: Solve the polynomial inequality {{{x^3+5x^2-9x-45 >= 0}}}

Question 363748: Solve the polynomial inequality

Answer by Sphinx pinastri(17) (Show Source): You can put this solution on YOUR website!
Solve the polynomial inequality

First, we need to factor the polynomial. Solving the equation
using Cardano formula is rather difficult. Let's look for an
integer root first.
It's well known that the integer root of a polynomial with integer
coefficients is a divider of the constant term. A quick check shows
that 3 is a root.
Now, the original polynomial can be divided by (x-3).

By solving the square equation, we get

The polynomial is positive when x is large, the graph intersects
X axis at 5 and touches it at 3.
So the answer is:

and

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