Calculadora de Zeros Racionais

The Rational Zeros Calculator applies the Rational Root Theorem to find all possible rational roots of a polynomial with integer coefficients. Given a polynomial P(x) = a·xⁿ + … + c, where a is the leading coefficient and c is the constant term, it computes the divisors of c and a, then generates all combinations ± (divisor of c)/(divisor of a). The result is a list of candidate rational roots, which can be tested in the polynomial to verify if they are actual roots.

The operation is simple: the user enters the coefficients of the polynomial, from the highest degree term to the constant term. The tool automatically identifies the leading coefficient (a) and constant term (c), calculates their integer divisors (positive and negative), and combines them as fractions. For example, for P(x) = 2x³ - x² - 4x + 2, divisors of c=2 are ±1, ±2 and divisors of a=2 are ±1, ±2. Possible rational roots are ±1, ±2, ±1/2.

This calculator is useful for students and professionals who need to factor polynomials or solve polynomial equations. It speeds up the process of finding rational roots, which is the first step for complete factorization. Use it in algebra, calculus, or engineering problems involving polynomials. Remember that the theorem only guarantees rational roots; irrational or complex roots are not listed.

Important precautions: the polynomial must have integer coefficients. If there are fractional coefficients, multiply the entire polynomial by the least common multiple of the denominators. Also, the generated list contains only candidates; not all will be actual roots of the polynomial. Each candidate must be tested (for example, using the Remainder Theorem) to confirm. The calculator also does not handle repeated roots; if a root has multiplicity greater than 1, it will appear only once in the list.