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Chapter 9: Q21. (page 593)

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

6x2鈭�13x=15

Short Answer

Expert verified

The roots of the equation6x2鈭�13x=15 arex=鈭�0.8 and x=3.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, fx=ax2+bx+c, where,a鈮�0 is called the standard form of the quadratic function.

02

 Step 2. Rewrite the equation + in the form +. 

Write the equation 6x2鈭�13x=15 in standard form.

This standard form is

6x2鈭�13x鈭�15=0

Write the equation 6x2鈭�13x鈭�15=0 in the form fx=ax2+bx+c.

fx=6x2鈭�13x鈭�15

03

Step 3. Plot the graph of the function fx=6x2−13x−15.

The graph of the function fx=6x2鈭�13x鈭�15is shown below.

04

Step 4. Solve the equation 6x2−13x=15 from the graph of the function fx=6x2−13x−15. 

Observe the graph of the function fx=6x2鈭�13x鈭�15.

The graph intersects the x-axis at the points near about x=鈭�0.8and x=3.

Therefore the roots of the equation x2鈭�10x=鈭�21 are x=鈭�0.8 and x=3.

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Most popular questions from this chapter

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

鈭�x2+3x鈭�1=0

Consider y=x2鈭�5x+4

Find the coordinates of the vertex. Is it a maximum or minimum point?

Solve each equation by completing the square.

x2+2x+5=0

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REASONING Provide a counterexample to the following statement. The vertex of a parabola is always the minimum of the graph.
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