💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

In Exercises 1–3, the graph of a quadratic function ƒ is given. Use the graph to find the solution set of each equation or inequality. See Example 1.(a) $3 x^{2}+10 x-8=0$(b) $3 x^{2}+10 x-8 \geq 0$(c) $3 x^{2}+10 x-8<0$

(a) \{-2,5\}(b) [-2,5](c) $(-\infty,-2] \cup[5, \infty)$

Precalculus

Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 8

Polynomial and Rational Inequalities

Introduction to Conic Sections

Equations and Inequalities

Functions

Polynomials

Missouri State University

McMaster University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

04:42

In Exercises 1–3, the grap…

03:16

02:17

The graph of a quadratic f…

02:36

02:19

02:31

For Exercises $3-6,$ use t…

02:07

Solve each inequality anal…

09:26

0:00

Determine whether each val…

02:08

In Exercises 13 - 30, s…

02:34

02:20

01:54

Graph each quadratic funct…

01:43

Solve each quadratic inequ…

01:06

02:16

02:12

In Exercises 5 - 8, det…

02:01

Solve each polynomial ineq…

02:04

02:54

right. So we want to talk about when the function negative X squared, plus three x plus 10. To start, we're gonna talk about where it's equal to zero, and I think it's pretty easy to see when we can look at the graph that we have Roots at X equals negative two and at X equals five. So there will be our solution set some next we want to look at when negative X squared plus three X plus 10 is greater than or equal to zero. Once again, we can look at our graph where the roots are at negative two and positive five. And we want to know when this function is greater than or equal to zero. Well, we're nowhere equals zero at negative 215 We're also gonna be greater than zero when were above the X access. So that's going to be on that interval between the negative two and the five. So the solution set will be the interval from negative to 25 and we want to use the brackets and the parentheses because the negative to in the five are included as part of the solution set. In other words, what we're saying here is negative two is less than or equal to acts and acts was less than or equal to five. The last thing that we want to consider then, for this question, is when negative X squared plus three acts plus 10 is less than or equal to zero. Well, once again, looking at the graph, we have this curve that's doing something kind of like this. My roots are still at negative two and that positive five. But we want to know when were equal to or less than zero. Well, we're gonna be less than zero when were below the X axis. So in other words, on the x axis that's gonna be one were to the left of negative too, and to the right of five. So we're gonna have the interval from negative infinity, too. Negative, too. And again, I'm including the negative two is part of the solution set because I want to know when I'm equal to zero or the interval from five to infinity

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

In Exercises 1–3, the graph of a quadratic function ƒ is given. Use the grap…

The graph of a quadratic function $f$ is given. Use the graph to find the so…

For Exercises $3-6,$ use the graph of the function to solve each inequality.…

Solve each inequality analytically. Support your answers graphically. Give e…

Determine whether each value of $x$ is a solution of the inequality.Ineq…

In Exercises 13 - 30, solve the inequality and graph the solution o…

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, an…

Solve each quadratic inequality by locating the $x$ -intercept(s) (if they e…

Solve each quadratic inequality. Graph each solution.$$3 a^{2}+a>…

In Exercises 5 - 8, determine whether each value of is a solution …

Solve each polynomial inequality and graph the solution set on a real number…

00:18

Simplify by first converting to rational exponents. Assume that all variable…

00:31

Find each power of $i$$$i^{38}$$

00:39

Solve each problem. See Example 11.Use the formula in Example 11 to calc…

00:16

00:45

Let $f(x)=x^{2}-9, g(x)=2 x,$ and $h(x)=x-3 .$ Find each of the following. S…

01:28

Which point lies on the graph of $f(x)=3^{x} ?$A. $(1,0)$B. $(3,1)$<…

00:20

Simplify each expression. Write all answers with positive exponents. Assume …

01:38

The Greeks had a method of completing the square geometrically in which they…

00:32

Simplify each radical. Assume that all variables represent positive real mum…

00:28

Find each power of $i$$$i^{43}$$