Descartes' Rule of Signs Calculator

Your details

The highest power of x in your polynomial.
Coefficient of the x^3 term.
Coefficient of the x^2 term.
Coefficient of the x term.
The constant term (coefficient of x^0).
Max positive real roots
2

Upper bound on positive real roots (sign changes in f(x))

Max negative real roots1
Min complex (non-real) roots0
Possible root combinations2
Max positive real roots2
Max negative real roots1
Min complex roots0

2 root combinations are possible: up to 2 positive and up to 1 negative real roots.

  • There are at most 2 positive real roots. The actual count is 2, 0, ..., down to 1 or 0 (decreasing by 2 each time).
  • There is exactly 1 negative real root.

Next stepDescartes' Rule gives upper bounds, not exact counts. To find actual roots, use the Rational Root Theorem to test candidate rational roots, or apply numerical methods such as Newton's method.

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