IXL - Solve quadratic inequalities (Algebra 2 practice)

Solve for

(

–

)

(

)

Write a compound inequality like 1 < x < 3 or like x < 1 or x >

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Learn with an example

question

Solve for

(

–

)

(

–

)

Write a compound inequality like 1 < x < 3 or like x < 1 or x >

key idea

A polynomial inequality can be written as

(

)

(

)

≥

(

)

(

)

≤

where

(

)

is a polynomial.

The roots of

(

)

separate the

-axis

into intervals. On each interval,

(

)

is either entirely positive or entirely negative.

This diagram is called a sign chart. It shows whether

(

)

is positive or negative on each interval between its roots. (In this example,

(

)

(

–

)

(

–

)

solution

Look at the polynomial inequality:

(

–

)

(

–

)

Since the inequality is strict (<), the solution to the inequality is the set of values where the polynomial

(

–

)

(

–

)

is negative.

Create a sign chart.

Start by marking the roots of the polynomial on a number line. You can find the roots by solving

(

–

)

(

–

)

The roots are 2 and 6.

The roots separate the number line into intervals. Find the sign of each factor on each interval.

The factor
x
–
2
is negative if
x
<
2
and positive if
x
>
2
.
The factor
x
–
6
is negative if
x
<
6
and positive if
x
>
6
.

Summarize this information in a table. Then, multiply the signs in each column to determine the sign of

(

–

)

(

–

)

on each of the intervals.

	x < 2	2 < x < 6	x > 6
x – 2	-	+	+
x – 6	-	-	+
( x – 2 ) ( x – 6 )	+	-	+

The last row of the table shows that

(

–

)

(

–

)

is positive when

negative when

and positive when

Write the solution.

The solution is the set where the polynomial is negative.

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.9Graph solutions to quadratic inequalities

C.2Write inequalities from graphs

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