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Maths

Descartes' rule of signs calculator

Maximum possible positive and negative real roots of a polynomial, from its sign changes.

What this calculator does

Descartes' rule of signs works out maximum possible positive and negative real roots of a polynomial, from its sign changes. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

FormulaPositive real roots ≤ sign changes in p(x); negative real roots ≤ sign changes in p(−x); each count can drop by an even number

The inputs explained

FieldWhat to enter
Coefficients, highest degree first (e.g. 1,-6,11,-6 for x³−6x²+11x−6)A list of numbers, separated by commas or spaces.