Mathematica Tutorial

Numerical Solution of Polynomial Equations

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects.

You can get numerical solutions by applying N.

This gives the numerical solutions to 25-digit precision.

You can use NSolve to get numerical solutions to polynomial equations directly, without first trying to find exact results.

NSolve[poly0,x]	get approximate numerical solutions to a polynomial equation
NSolve[poly0,x,n]	get solutions using n-digit precision arithmetic
NSolve[{eqn₁,eqn₂,...},{var₁,var₂,...}]
	get solutions to a polynomial system

Numerical solution of polynomial equations and systems.

NSolve will give you the complete set of numerical solutions to any polynomial equation or system of polynomial equations.

NSolve can find solutions to sets of simultaneous polynomial equations.