Chapter 9: Q6. (page 597)

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$x^{2} + 7 x + 10 = 0$

Short Answer

Expert verified

The solutions of the equation are $- 5$ and $- 2$ .

Step by step solution

Step 1. Graph the equation.

Graph theequation $y = x^{2} + 7 x + 10$ to find the roots.

Step 2. State the interpretation of the graph.

In the graph of the equation $y = x^{2} + 7 x + 10$ it can be observed that the x-intercepts appear to be at $- 5$ and $- 2$ , therefore, the solutions are $- 5$ and $- 2$ .

Step 3. Check the solutions.

To check the solutions first substitute $- 5$ for $x$ into the equation $y = x^{2} + 7 x + 10$ and simplify.

$\begin{array}{c} x^{2} + 7 x + 10 \overset{?}{=} 0 \\ {(- 5)}^{2} + 7 (- 5) + 10 \overset{?}{=} 0 \\ 25 - 35 + 10 \overset{?}{=} 0 \\ 10 - 10 \overset{?}{=} 0 \\ 0 \overset{?}{=} 0 True \end{array}$

Now substitute $- 2$ for $x$ into the equation $y = x^{2} + 7 x + 10$ and simplify.

role="math" localid="1647860259595" $\begin{array}{l} x^{2} + 7 x + 10 \overset{?}{=} 0 \\ {(- 2)}^{2} + 7 (- 2) + 10 \overset{?}{=} 0 \\ 4 - 14 + 10 \overset{?}{=} 0 \\ 14 - 14 \overset{?}{=} 0 \\ 0 \overset{?}{=} 0 True \end{array}$

Therefore, the solutions of the equation are $- 5$ and $- 2$ .

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Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$x^{2} + 7 x + 10 = 0$

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. State the interpretation of the graph.

Step 3. Check the solutions.

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Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.x2+7x+10=0

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. State the interpretation of the graph.

Step 3. Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.
$x^{2} + 7 x + 10 = 0$