1Cademy - Quadratic Equation

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Algebraic Equation

Definition

Quadratic Equation

A quadratic equation is an equation in which the variable is squared. Its general form is:

$ax^2 + bx + c = 0$

where $a$ , $b$ , and $c$ are real numbers and $a \neq 0$ . The requirement that $a \neq 0$ is essential — without a squared term, the equation would be linear rather than quadratic. This distinguishes quadratic equations from linear equations, where variables appear only to the first power and have no exponents.

Examples of quadratic equations include $x^2 + 5x + 6 = 0$ , $3y^2 + 4y = 10$ , $64u^2 - 81 = 0$ , and $n(n + 1) = 42$ . An equation like $n(n + 1) = 42$ may not initially appear to be quadratic, but simplifying the left side produces $n^2 + n$ , revealing the squared variable. Solving quadratic equations requires methods different from those used for linear equations.

Updated 2026-04-21

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