Find all roots of any polynomial up to degree 6.
For x³−6x²+11x−6, enter: 1, -6, 11, -6 (highest power first)
For degree ≤ 2, use exact formulas. For higher degrees, numerical methods like Laguerre's method or Newton's method are used. A polynomial of degree n has exactly n roots (counting multiplicities) by the Fundamental Theorem of Algebra.
Every non-constant polynomial with complex coefficients has at least one complex root. This means a polynomial of degree n has exactly n roots in the complex number system (counting multiplicity).
Enter coefficients from the highest degree term to the constant term, separated by commas. For 2x⁴ + 0x³ − 5x² + 3x − 1, enter: 2, 0, -5, 3, -1.
Yes. A polynomial can have repeated roots (roots with multiplicity > 1). For example, (x−2)³ = x³−6x²+12x−8 has x = 2 as a root of multiplicity 3.