/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 Find the zeros of the function a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

Find the zeros of the function algebraically. $$f(x)=3 x^{2}+22 x-16$$

Short Answer

Expert verified
The zeros of the function are \( x = \frac{2}{3} \) and \( x = -8 \).

Step by step solution

01

Identify Coefficients

Identify the coefficients \(a\), \(b\), and \(c\) from the equation. Here \(a = 3\), \(b = 22\), and \(c = -16\) in the equation \(f(x) = 3x^{2} + 22x - 16\).
02

Substitute Coefficients in Quadratic Formula

Substitute these coefficients into the quadratic formula: \( x= \frac{-22 \pm \sqrt{(22)^{2}-4*3*(-16)}}{2*3} \) .
03

Simplify the Equation

Simplify this equation to solve for \(x\). This simplifies to: \( x= \frac{-22 \pm \sqrt{484 +192}}{6} \) . Then further simplify to: \( x = \frac{-22 \pm \sqrt{676}}{6} = \frac{-22 \pm 26}{6} \) .
04

Solve for x

Now solve for \(x\) by separately considering the plus and minus signs. This gives \( x = \frac{4}{6} \) or \( x = -8 \) . Simplifying the first solution for \(x\) gives \( x = \frac{2}{3} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Simple Interest The simple interest on an investment is directly proportional to the amount of the investment. An investment of \(\$ 6500\) will earn \(\$ 211.25\) after 1 year. Find a mathematical model that gives the interest \(I\) after 1 year in terms of the amount invested \(P\).

(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$k(x)=4\left(\frac{1}{2} x-\left[\left[\frac{1}{2} x\right]\right]\right)^{2}$$

The cost of sending an overnight package from New York to Atlanta is 26.10 dollars for a package weighing up to, but not including, 1 pound and 4.35 dollars for each additional pound or portion of a pound. (a) Use the greatest integer function to create a model for the cost \(C\) of overnight delivery of a package weighing \(x\) pounds, \(x>0\). (b) Sketch the graph of the function.

For groups of 80 or more people, a charter bus company determines the rate per person according to the formula Rate \(=8-0.05(n-80), \quad n \geq 80\) where the rate is given in dollars and \(n\) is the number of people. (a) Write the revenue \(R\) for the bus company as a function of \(n\) (b) Use the function in part (a) to complete the table. What can you conclude? $$\begin{array}{|l|l|l|l|l|l|l|l|}\hline n & 90 & 100 & 110 & 120 & 130 & 140 & 150 \\\\\hline R(n) & & & & & & & \\\\\hline\end{array}$$

Determine whether the statement is true or false. Justify your answer. The set of ordered pairs \(\\{(-8,-2),(-6,0),(-4,0)\) \((-2,2),(0,4),(2,-2)\\}\) represents a function.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.