/*! 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 9 Find the key numbers of the expr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 9

Find the key numbers of the expression. $$3 x^{2}-x-2$$

Short Answer

Expert verified
The key numbers of the expression are \(x_1 = 1\) and \(x_2 = -\frac{2}{3}\)

Step by step solution

01

Identify Coefficients

The equation can be written in the form \(ax^2 + bx + c = 0\), where \(a = 3\), \(b = -1\), and \(c = -2\). Coefficients \(a\), \(b\), and \(c\) are necessary in applying the quadratic formula.
02

Apply the Quadratic Formula

The quadratic formula \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] is applied with \(a = 3\), \(b = -1\), and \(c = -2\). This solves for the values of \(x\), which are the key numbers of the equation.
03

Calculate the Discriminant

The term \(b^2 - 4ac\) is the discriminant, which determines the type and number of solutions. Substitute \(a = 3\), \(b = -1\), and \(c = -2\) into the discriminant, then calculate its value.
04

Perform the Final Calculation

Substitute the discriminant and the coefficients into the quadratic formula to find the values of \(x\). These are the key numbers of the quadratic equation.

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

Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=f(2 x)$$

Geometry You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides. (a) Let \(x\) represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box. (b) Use the diagram to write the volume \(V\) of the box as a function of \(x .\) Determine the domain of the function. (c) Sketch the graph of the function and approximate the dimensions of the box that will yield a maximum volume. (d) Find values of \(x\) such that \(V=56 .\) Which of these values is a physical impossibility in the construction of the box? Explain.

The revenue and cost equations for a product are \(R=x(50-0.0002 x)\) and \(C=12 x+150,000,\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 1,650,000 ?\) What is the price per unit?

Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-3 x^{3}-x^{2}-12 x-20\) (Hint: One factor is \(\left.x^{2}+4 .\right)\)

Prove that the complex conjugate of the sum of two complex numbers \(a_{1}+b_{1} i\) and \(a_{2}+b_{2} i\) is the sum of their complex conjugates.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

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.