Problem 155 - Algebra and Trigonometry

Question

What is a quadratic equation?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.