Inequality question: x^3 + 2x^2 -19x - 20 > 20?

Question

Solve the following polynomial inequality

Answer 1

The inequality x ³  + 2x ² -19x -20 > 20

The first thing to do get a zero on one side and factor the polynomial if possible.

x ³  + 2x ² -19x -20 -20 > 0

x ³ + 2x ² - 19x  - 40 > 0

Now find real zeros of x ³ + 2x ² - 19x  - 40 = 0

Graph

The points where the curve crosses the x - axis will give solution to the equation .

The graph crosses the x  - axis at a point that would suggest a solution of the equation.

It crosses the x  - axis at three points , hence there are 3 real roots.

Use synthatic division to detrmine if the given values of x  are roots of the polynomial.

Since f (4.39) = 0 , x  = 4.39 is a zero.

Since f (-4.25) = 0, x  = -4.25 is a zero.

Since f (-2.13) = 0, x  = -2.13 is a zero.

Factoring of the polynomial is (x  + 2.13)(x  + 4.25)(x  - 4.39).

x ³ + 2x ² - 19x  - 40 > 0

And from the graph observe the intervals where it is greater than zero.

From -4.25 to -2.13 and

From 4.39 on

x ³  + 2x ² - 19x  - 40 > 0

Solutions

x  > 4.39

-4.25 < x  < -2.13