Examples for

Numerical Root Finding

Wolfram|Alpha provides flexible tools for numerical root finding using algorithms, such as Newton's method and the bisection method. Pick starting points, precision and method. Explore complex roots or the step‐by‐step symbolic details of the calculation.

Newton's Method

Compute the roots of an equation or number with Newton's method.

Find a root of an equation using Newton's method:

Specify a starting point:

Specify precision:

Find a complex root with Newton's method:

Compute the nth root of a number using Newton's method:

Bisection Method

Calculate the roots of an equation using the bisection method.

Find a root of an equation using the bisection method:

Compute the nth root of a number using the bisection method:

Secant Method

Use the secant method for numerical root finding.

Find a root of an equation using the secant method:

Compute the nth root of a number using the secant method: