Polynomial Graphing Calculator
The polynomial graphing calculator is here to help you with one-variable polynomials up to degree four. It not only draws the graph, but also finds the functions roots and critical points (if they exist).
Rational roots found1, 2, 3
Polynomialx^3 - 6x^2 + 11x - 6degree 3
Candidates tested8
Descartes: positive rootsat most 3sign changes in P(x)
Descartes: negative rootsat most 0sign changes in P(−x)
Leading / constant1 / -6
The method
candidates are ± (factors of the constant) ÷ (factors of the leading coefficient)
The rational root theorem
If a polynomial with integer coefficients has a rational root p/q in lowest terms, then p divides the constant term and q divides the leading coefficient. That turns an infinite search into a short finite list.
It says nothing about irrational or complex roots — those simply will not appear in the list, which is why a polynomial can have no rational roots at all.