How to Determine The Quadratic Inequality Settlement Set

Definition of Quadratic Inequality

Quadratic inequality is the inequality with the highest rank of the variable is two. The set of inequality settlements can be written in the form of a set notation or by a number line.

How to Determine The Quadratic Inequality Settlement Set

The steps for finding the settlement set of quadratic inequalities are as follows:

Express the quadratic inequalities in the form of quadratic equations (right side = 0).
Look for the roots of the equation.
Draw a line of numbers that contains the roots.
Determine the sign (positive or negative) at each interval by testing the marks of each interval.
The settlements set is obtained from the intervals that satisfy the inequalities.

Example:
Determine the settlements set from x² - 2x - 8 > 0 !

Answer:

1. Express the quadratic inequalities in the form of quadratic equations (right side = 0).
x² - 2x - 8 > 0 Become:
x² - 2x - 8 = 0

2. Look for the roots of the equation
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x =-2

3. Draw a line of numbers that contains the roots.

The line of numbers is divided into three intervals ie the left, center, and right intervals.

4. Determine the sign (positive or negative) at each interval by testing the marks of each interval, then test the sign.

From the table obtained:

Interval containing -3 is marked (-)
Interval containing 0 marked (+)
Interval containing 5 marked (-)

5.The settlements set is obtained from the intervals that satisfy the inequalities.
Because on the matter that the inequality sign is more than (>), then to solve taken the interval of positive sign (+), such as: