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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 with a degree of 2. It has the general form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a\) cannot be 0.

Step by step solution

01

Defining a Quadratic Equation

A quadratic equation is a second-order polynomial equation in a single variable x with a degree of 2. It is an equation that can be written in the standard form as \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(x\) represents an unknown.
02

Explaining the General Form

In the general form of a quadratic equation \(ax^2 + bx + c = 0\), \(a\), \(b\), and \(c\) are constants. \(a\) cannot be 0 because it would make the equation linear, not quadratic. \(x\) is the variable or the solution to the equation.
03

Describing the Components

The terms a, b, and c in the quadratic equation are known as coefficients. The coefficient \(a\) is referred to as the quadratic coefficient, \(b\) as the linear coefficient, and \(c\) as the constant or free term.

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