Rational Root Calculator
Find all possible rational roots of a polynomial using the Rational Root Theorem.
Enter Polynomial
For 2x² - 7x + 3, enter: 2, -7, 3
P(x) =
2x^2 - 7x + 3
Leading coefficient (a₀)
2
Factors: 1, 2
Constant term (aₙ)
3
Factors: 1, 3
Results
Possible Rational Roots (±p/q)
-3, -1.5, -1, -0.5, 0.5, 1, 1.5, 3
Actual Rational Roots
x = 0.5, 3
P(-3) = 42
P(-1.5) = 18
P(-1) = 12
P(-0.5) = 7
P(0.5) = 0ROOT
P(1) = -2
P(1.5) = -3
P(3) = 0ROOT
Rational Root Theorem
The Theorem
If a polynomial P(x) = aₙxⁿ + ... + a₁x + a₀ with integer coefficients has a rational root p/q (in lowest terms), then p divides a₀ and q divides aₙ.
Formula
Possible roots = ± (factors of constant) / (factors of leading coef)