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:

using Newton's method solve x cos x = 0

Specify a starting point:

newton-raphson x^3 - 15x + 10 start at 2.25

Specify precision:

solve x^5-2 using newton method with x0=2 to 50 digits

Find a complex root with Newton's method:

Newton's method sin z = 4
use Newton's method to solve x^5-2 with x0=2I

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

using Newton's method find (53)^(1/3)
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Secant Method

Use the secant method for numerical root finding.

Find a root of an equation using the secant method:

using secant method solve x^3-2 at x1=-3 and x2=3

Compute the n th root of a number using the secant method:

using secant method find root of 7
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Bisection Method

Calculate the roots of an equation using the bisection method.

Find a root of an equation using the bisection method:

solve sin(1/x)=0 using the bisection method
using bisection method solve x cos x at a=1 and b=4 with 20 digits precision

Compute the n th root of a number using the bisection method:

find root of 2 with bisection method
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