How to use this calculator
Zeros are inputs where a function evaluates to zero. On a graph they correspond to x-axis crossings or touches. This tool accepts a polynomial coefficient list, isolates real roots using derivative information, and reports a substitution residual for each numerical result.
The method
Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.
Polynomial coefficients: 1, -6, 11, -6
Zeros of the polynomial: 1, 2, 3
f(x) = x^3 - 6x^2 + 11x - 6
Scope and limitations
Polynomials only, through degree 6. Complex roots are returned for quadratics only. Numerical root finding can be sensitive to nearly repeated roots and poorly scaled coefficients; verify critical results independently.
Common questions
Can it find a root where the graph only touches the axis?
The solver also checks derivative critical points, allowing many repeated roots to be detected without a sign change.
Can I enter sin(x) or log(x)?
No. This version accepts polynomial coefficients. Dedicated trigonometric and logarithmic graphing tools are available.
References & further reading
External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.