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Chapter 4: Q. 2 (page 241)

Solve the inequality x2-5x鈮�24. Graph the solution set.

Short Answer

Expert verified

The solution set of given inequality is [-3,8]and its graph is

Step by step solution

01

Step 1. Using mathematical operations, solve the inequality.

First replace inequality symbol with an equality symbol.

x2-5x=24x2-5x-24=0

Now factorize the quadratic equation.

Find two terms whose sum is -5x and multiplication -24x2.

x2-8x+3x-24=0x(x-8)+3(x-8)=0

Taking common terms out.

(x-8)(x+3)=0gives

x-8=0orx+3=0x=8orx=-3

As the inequality was not strict in question, so the solution set ofx2-5x鈮�24will be-3鈮�x鈮�8or[-3,8].

02

Step 2. The graph to show the solution set of x2-5x≤24 is as follows.

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