/*! 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 155 What is a quadratic equation?... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 155

What is a quadratic equation?

Short Answer

Expert verified
A quadratic equation is a second-order polynomial equation in a single variable x. It has the general form \( ax^2 + bx + c = 0 \), where x represents an unknown, and a, b, and c are constants. The term 'quadratic' comes from 'quadra', which means 'square' in Latin; hence the primary defining characteristic of a quadratic equation is the presence of the \( x^2 \) term.

Step by step solution

01

Identify the Components of a Quadratic Equation

A quadratic equation is a second-order polynomial equation in a single variable. It is represented as \( ax^2 + bx + c = 0 \), where: - 'a' is the coefficient of \( x^2 \) (the quadratic term), and \( a \neq 0 \), - 'b' is the coefficient of x (the linear term), - 'c' is the constant.
02

Understand the Quadratic Term

The term \( ax^2 \) is known as the quadratic term. 'a' can be any number except 0 and the variable 'x' is always squared (that's why we call it 'quadratic', which stems from Latin 'quadra' meaning 'square'). The important thing to keep in mind is that without this squared term, the equation wouldn't be quadratic.
03

Understand the Linear Term and Constant

The term 'bx' is the linear term of the quadratic equation. 'b' can be any number (including 0). The last number 'c' is the constant term; again, 'c' can be any number (including 0).

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

In your own words, describe a step-by-step approach for solving algebraic word problems.

You invested \(\$ 7000\) in two accounts paying \(6 \%\) and \(8 \%\) annual interest. If the total interest earned for the year was \(\$ 520,\) how much was invested at each rate?

A machine produces open boxes using square sheets of metal. The figure illustrates that the machine cuts equal sized squares measuring 2 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 200 cubic inches, find the length and width of the open box.

Will help you prepare for the material covered in the next section. $$\text{Rationalize the denominator: }\frac{7+4 \sqrt{2}}{2-5 \sqrt{2}}$$

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y=2 x^{2}-3 x \text { and } y=2 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.