Chapter 3: Q. 18 (page 174)

In Problems 18–19, solve each quadratic inequality.
$x^{2} + 6 x - 16 < 0$

Short Answer

Expert verified

The solution of inequality is $\{x | - 8 < x < 2\}$ or interval notation $(- 8, 2)$ .

Step by step solution

Step 1. Given information.

Solve the given quadratic inequality.

$x^{2} + 6 x - 16 < 0$

Step 2. Graph the function.

Graph the function $f (x) = x^{2} + 6 x - 16$ .

Step 3. Find intercept.

y- intercept: $f (0) = 0^{2} + 6 (0) - 16 = - 16$

x-intercept : Solve $f (x) = 0$

$x^{2} + 6 x - 16 = 0 x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x_{1, 2} = \frac{- 6 \pm \sqrt{6^{2} - 4 \cdot 1 \cdot (- 16)}}{2 \cdot 1} x_{1, 2} = \frac{- 6 \pm \sqrt{36 + 64}}{2} x_{1, 2} = \frac{- 6 \pm \sqrt{100}}{2} x_{1, 2} = \frac{- 6 \pm 10}{2} x_{1} = \frac{- 6 + 10}{2}, x_{2} = \frac{- 6 - 10}{2} x_{1} = 2, x_{2} = - 8$

So, the x-intercept are $x_{1} = 2 and x_{2} = - 8$

The graph is below the x-axis $(f (x) < 0)$ between the $x = - 8 and x = 2$ . Since the inequality is strict the solution set is $\{x - 8 < x < 2\}$ or using interval notation $(- 8, 2)$ .

Step 4. Conclusion.

The solution set of inequality is $\{x - 8 < x < 2\}$ or interval notation $(- 8, 2)$ .

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In Problems 18–19, solve each quadratic inequality.
$x^{2} + 6 x - 16 < 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the function.

Step 3. Find intercept.

Step 4. Conclusion.

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In Problems 18–19, solve each quadratic inequality.x2+6x-16<0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the function.

Step 3. Find intercept.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 18–19, solve each quadratic inequality.
$x^{2} + 6 x - 16 < 0$