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Rational Root Theorem Calculator

Every ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.

Related tools

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Rational Equation SolverSolve rational (fraction) equations by clearing denominators to a polynomial, then excluding roots that make any denominator zero — reporting solutions, excluded values, no-solution and identity cases.Rational Expression CalculatorSimplify, add, subtract, multiply, divide, factor and decompose rational expressions in x — e.g. (x^2-1)/(x-1) → x+1 — using exact polynomial arithmetic and partial fractions.Digital Root CalculatorCompute the additive and multiplicative digital root of any number in base 2, 8, 10 or 16, with the full chain, the mod-9 shortcut and the persistence count.Nth root calculatorCompute any root (square, cube, nth) of a number.Cube root calculatorCompute the cube root of a number, plus its cube.Primitive root calculatorFind the primitive roots modulo n — the generators g whose powers g¹, g², … run through every number coprime to n before repeating (order equal to φ(n)). Primitive roots exist only when n is 1, 2, 4, pᵏ or 2pᵏ for an odd prime p; the tool reports the smallest one, the exact count φ(φ(n)) and lists them. They are the backbone of discrete-logarithm cryptography and Diffie–Hellman key exchange.Square root calculatorCompute the square root of a number, plus its square.Bayes Theorem CalculatorCompute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time.

Open Rational Root Theorem Calculator and you get an answer straight away, with no account to create. Its place is under Algebra & equations; Rational Equation Solver and Rational Expression Calculator answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Rational Root Theorem Calculator do?

Every ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Rational Root Theorem Calculator different from Rational Equation Solver?

They sit next to each other but answer different questions: Rational Equation Solver is the one to open when you need it to solve rational (fraction) equations by clearing denominators to a polynomial, then excluding roots that make any denominator zero — reporting solutions, excluded values, no-solution and identity cases. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Rational Expression Calculator is the closest one after this: Simplify, add, subtract, multiply, divide, factor and decompose rational expressions in x — e.g. (x^2-1)/(x-1) → x+1 — using exact polynomial arithmetic and partial fractions.

What else is worth having open alongside it?

Digital Root Calculator and Nth root calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.