Chapter 3: Q. 19 (page 174)

In Problems 18–19, solve each quadratic inequality.
$3 x^{2} \geq 14 x + 5$

Short Answer

Expert verified

The solution of inequality is $\{x x \leq - \frac{1}{3} or x \geq 5\}$ or interval notation $(- \infty, - \frac{1}{3}] or [5, \infty)$ .

Step by step solution

Step 1. Given information.

Solve the given quadratic inequality.

$3 x^{2} \geq 14 x + 5$

Step 2. Graph the function.

Rearrange the function.

$3 x^{2} \geq 14 x + 5 3 x^{2} - 14 x - 5 \geq 0$

Graph the function $f (x) = 3 x^{2} - 14 x - 5$

Step 3. Find intercept.

y- intercept: $f (0) = 3 {(0)}^{2} - 14 (0) - 5 = - 5$

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

$3 x^{2} - 14 x - 5 = 0 3 x^{2} - 15 x + x - 5 = 0 3 x (x - 5) + 1 (x - 5) = 0 (x - 5) (3 x + 1) = 0 x = 5, - \frac{1}{3}$

So, the x-intercept are $x_{1} = 5 and x_{2} = - \frac{1}{3}$

The solution set is $\{x x \leq - \frac{1}{3} or x \geq 5\}$ and in interval notation $(- \infty, - \frac{1}{3}] or [5, \infty)$ .

Step 4. Conclusion.

The solution set of inequality is $\{x x \leq - \frac{1}{3} or x \geq 5\}$ or in interval notation $(- \infty, - \frac{1}{3}] or [5, \infty)$ .

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x	$y = f (x)$
-2	-4
-1	0
0	4
1	8
2	12

In Problems 18–19, solve each quadratic inequality.
$3 x^{2} \geq 14 x + 5$

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.

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In Problems 18–19, solve each quadratic inequality.3x2≥14x+5

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

Probability and Statistics

Discrete Mathematics

Decision Maths

Pure Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 18–19, solve each quadratic inequality.
$3 x^{2} \geq 14 x + 5$