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Chapter 9: Q18. (page 594)

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

x2鈭�x鈭�12=0

Short Answer

Expert verified

The roots of the equationx2鈭�x鈭�12=0 arex=鈭�3 and role="math" localid="1647865845332" x=4.

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 x2−x−12=0 in the form fx=ax2+bx+c. 

Write the equation x2鈭�x鈭�12=0 in standard form.

This equation is already in standard form.

Write the equation x2鈭�x鈭�12=0 in the form fx=ax2+bx+c.

fx=x2鈭�x鈭�12

03

Step 3. Plot the graph of the function fx=x2−x−12.

The graph of the function is shown below.

04

Step 4. Solve the equation x2−x−12=0 from the graph of the function.  fx=x2−x−12

Observe the graph of the function fx=x2鈭�3x鈭�4.

The graph intersects the x-axis at the points x=鈭�3and x=4.

Therefore the roots of the equation x2鈭�3x鈭�4=0 are x=鈭�3 and x=4.

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Most popular questions from this chapter

Consider y=x2鈭�5x+4

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Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

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y=7x2鈭�28x+14
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