How to Use Descartes' Rule of Signs Calculator
The Descartes' Rule of Signs Calculator accepts a polynomial in x. Enter f(x), and the Descartes' Rule of Signs Calculator lists the coefficient signs for f(x) and f(-x), counts sign changes, and returns possible positive and negative real root counts.
It also shows the coefficient sequences so you can check the reasoning step by step.
Formula & Theory — Descartes' Rule of Signs Calculator
The Descartes' Rule of Signs Calculator uses the rule that sign changes in f(x) give the maximum number of positive real roots. Sign changes in f(-x) give the maximum number of negative real roots.
Actual counts may be lower than the maximum by an even number. The Descartes' Rule of Signs Calculator lists all allowed counts rather than only the maximum.
Use Cases for Descartes' Rule of Signs Calculator
Use the Descartes' Rule of Signs Calculator for algebra, polynomial equations, real-root estimation, test preparation, and checking sign-sequence work. It is useful before graphing or applying numerical root-finding methods.