Polynomial roots
The calculator solves polynomial roots of any degree. For small degree polynomials analytic methods are applied, for 5degree or higher the polynomial roots are estimated by numerical method.
The calculator solves real polynomial roots of any degree univariate polynomial with integer or rational terms. The calculator factors an input polynomial into several squarefree polynomial, then solves each polynomial either analytically or numerically (for 5degree or higher polynomials). A function graph is plotted to illustrate the polynomial solution.
Polynomial coefficients, space separated.
Input polynomial
Even
Odd
Factorization
Real roots
Graph
Save the calculation to reuse next time, to extension embed in your website or share share with friends.
Ndegree polynomial real root calculation algorithm
 Check whether the input polynomial even or odd  the polynomial is even if f(x) = f(x), the polynomial is odd if f(x)=f(x).
 Factor the polynomial into squarefree polynomials with Yun algorithm Squarefree polynomial factorization.
 Every ndegree polynomial obtained is solved analytically if n<5:

 For 1stdegree  the root is the negative free term divided by the x coefficient

 2nd degree is solved by Solution of quadratic equation

 3rd degree: Cubic equation

 4th degree: Quartic equation solution
 Use numeric methods If the polynomial degree is 5 or higher

 Isolate the root bounds by VASCF algorithm: Polynomial root isolation. Find the roots in the positive field only if the input polynomial is even or odd (detected on 1st step)

 For each isolation bound find the approximate root value using numeric method: Bisection method

 Add the negative roots to the result set if the input polynomial is even or odd.
Comments