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Chapter 9: Q20. (page 593)

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

x2鈭�10x=鈭�21

Short Answer

Expert verified

The roots of the equation x2鈭�10x=鈭�21 are x=3 and x=7.

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 x2−10x=−21 in the form fx=ax2+bx+c. 

Write the equation x2鈭�10x=鈭�21 in standard form.

This equation is already in standard form.

Write the equation x2鈭�10x+21=0 in the form fx=ax2+bx+c.

fx=x2鈭�10x+21

03

Step 3. Plot the graph of the function fx=x2−10x+21.

The graph of the functionfx=x2鈭�10x+21 is shown below.

04

Step 4. Solve the equation x2−10x=−21 from the graph of the function fx=x2−10x+21. 

Observe the graph of the function fx=x2鈭�10x+21.

The graph intersects the x-axis at the points x=3 and x=7.

Therefore, the roots of the equation x2鈭�10x=鈭�21 are x=3 and x=7.

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Most popular questions from this chapter

Which is an equation for the function shown in the graph?

Ay=鈭�3x2

By=3x2+1

Cy=x2+2

Dy=鈭�3x2+2

Graph each function. Find the y-intercept, and state the domain and range.

y=3x+1

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

a2+12a+36

Consider y=x2鈭�5x+4

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

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

x2鈭�12x+32
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