Functions
AI Assistant

Root Finder

Find where any function crosses zero — graphically and instantly

A root (or zero) of a function f(x) is any value of x where f(x) = 0 — i.e., where the graph crosses or touches the x-axis.

This tool handles any function: polynomials, trigonometric, exponential, logarithmic, or mixed. Type the function into the chat, and the AI plots it, finds all roots in the current viewport, and labels each one with its exact x-value.

For complex functions with many roots (like sin(x)), zoom out or specify a range — the finder scans the visible viewport automatically. Ask the AI to explain what each root means mathematically.

Graph

FAQ

What is the difference between a root and an x-intercept?
They're the same thing. A root (or zero) of f(x) is a value r where f(r) = 0. Geometrically, this is exactly where the graph crosses the x-axis — the x-intercept. The two terms are used interchangeably.
Can this find roots of sin(x), ln(x), or mixed functions?
Yes. The root finder uses numerical methods that work on any continuous function — polynomial, trigonometric, exponential, or mixed. For functions with infinitely many roots (like sin(x)), it finds all roots in the current viewport. Zoom out to find more.
What if my function has no roots in the view?
Ask the AI to zoom out or try a wider viewport. Some functions like x² + 1 or eˣ have no real roots at all — the AI will tell you this and explain why.
How accurate are the roots?
Roots are found to 4 decimal places using a combination of sign-change scanning and bisection refinement. For most problems this is more than sufficient. For very close roots (within 0.001 of each other), the finder may merge them — try zooming in.
What is Newton's method for finding roots?
Newton's method (Newton-Raphson) is an iterative root-finding algorithm: starting from a guess x₀, it repeatedly updates x_{n+1} = x_n − f(x_n)/f'(x_n) until convergence. This site uses a simpler bisection approach for robustness, but Newton's method is faster when it converges.

Related Topics

Quadratic Formula CalculatorCubic Roots SolverFunction Intersection Calculator