Extraneous Root Definition (Illustrated Mathematics Dictionary)

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Math is Fun ABCDEFGHIJKLMNOPQRSTUVWXYZ Definition of Extraneous Root more ... Extraneous Root

A solution to an equation that SEEMS to be right, but when we check it (by substituting it into the original equation) we find it is NOT right.

Example: imagine we discover two possible roots "a" and "b" where an equation should equal zero. When we put "a" into the original equation we get zero. When we put "b" into the original equation we do NOT get zero. So "b" is an extraneous root.

This often happens when we square both sides during our solution.

See: Root, Equation, Solution Solving Radical Equations Copyright © 2025 Rod Pierce

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