What Are Quadratic Inequalities?

Quadratic inequalities are polynomial inequalities of degree 2. You solve them using sign charts. This is how to do it:

Rule

Solving Quadratic Inequalities

1.
Rearrange the inequality to get 0 is on the right-hand side.
2.
Rearrange the expression on the left-hand side in order of descending degree.
3.
Factorize the expression.
4.
Make a sign chart.
5.
Read off the solution.

Example 1

Solve the inequality x2 4 3x

x2 4 3x x2 3x 4 0 You can factorize this by using the quadratic formula: (x 4)(x + 1) 0

Next, you make a sign chart:

The sign charts of x-4 and x+1 are combined to create the sign chart of (x-4)(x+1)

You can read off that x2 4 3x when x (,1] [4,). Because we had a greater than or equal sign ( ) in the original inequality, the intervals are closed on the side that does not tend to infinity.

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