Work out rational root theorem instantly with clear inputs, formula shown and shareable results.
The rational root theorem says any rational root p/q in lowest terms must have p dividing the constant term and q dividing the leading coefficient. That reduces an infinite search to a short finite list.
Rational root theorem
possible roots = ±(divisor of the constant) / (divisor of the leading coefficient)
Candidates are ±1, ±2, ±3, ±6, ±½, ±3/2, and the actual rational roots are 2, −3 and ½.
The polynomial has no rational roots; its real roots are irrational and need numerical methods or surd forms.