Business Mathematics and Basic Statistics · Ch 1 — Quadratic Equations

General Form of a Quadratic Equation

A quadratic equation in one variable $x$ is an equation of degree 2, written in its general form as

p(x) = ax^2 + bx + c = 0, \quad a, b, c \in \mathbb{R}, \; a \neq 0

Here $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ , and $c$ is the constant term. The condition $a \neq 0$ is essential — if $a = 0$ , the $x^2$ term disappears and the equation reduces to the linear equation $bx + c = 0$ , which is no longer a quadratic.

Note

Why $a \neq 0$ is Non-Negotiable

The word "quadratic" itself comes from "quad," meaning square — the defining feature of a quadratic equation is the presence of the squared term $x^2$ with a non-zero coefficient. Every rule in this chapter (two roots, the discriminant, Sridharacharya's method) assumes $a \neq 0$ from the start.

Examples of quadratic equations in general form: $2x^2 + 5x - 3 = 0$ (here $a=2, b=5, c=-3$ ), $x^2 - 9 = 0$ (here $a=1, b=0, c=-9$ ), and $3x^2 - 12x = 0$ (here $a=3, b=-12, c=0$ ). Notice that $b$ or $c$ may individually be zero — only $a$ can never be zero.

A business-mathematics student meets this same quadratic form again later in the course wherever a relationship between two quantities is not a straight line — for instance, a cost or revenue expression that depends on the square of a quantity produced. This WBCHSE Class 11 Business Mathematics and Basic Statistics chapter builds the pure algebraic toolkit — factorization, perfect squares, and Sridharacharya's formula — that such later applications rely on.

Definition 1Quadratic equation (general form)

An equation of the form $ax^2 + bx + c = 0$ where $a, b, c$ are real numbers and $a \neq 0$ . The equation has degree exactly 2 in $x$ .

Next · 2 →Zeros (Roots) of a Quadratic Polynomial