Finding polynomial equation with roots given calculator

The calculator solves polynomial roots of any degree. For small degree polynomials analytic methods are applied, for 5-degree 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 square-free polynomials, then solves each polynomial either analytically or numerically (for 5-degree or higher polynomials). A function graph is plotted to illustrate the polynomial solution.

Finding polynomial equation with roots given calculator

N-degree polynomial roots

Polynomial coefficients, space separated.

Calculation precision

Digits after the decimal point: 5

The file is very large. Browser slowdown may occur during loading and creation.

Graph

The file is very large. Browser slowdown may occur during loading and creation.

N-degree 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 square-free polynomials with Yun algorithm Squarefree polynomial factorization.
  • Every n-degree polynomial obtained is solved analytically if n<5:
    • For 1st-degree - 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 VAS-CF 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 the numeric method: Bisection method
    • Add the negative roots to the result set if the input polynomial is even or odd.

Similar calculators

  • • Polynomial root isolation
  • • Polynomial math
  • • Greatest common divisor of several polynomials
  • • Resultant
  • • Squarefree polynomial factorization
  • • Algebra section ( 109 calculators )

 PLANETCALC, Polynomial roots

Polynomial Equation Solver Calculator is a free online tool that displays the value of the unknown variable by solving the given polynomial equation. BYJU’S online polynomial equation solver calculator tool makes the calculation faster, and it displays the variable value in a fraction of seconds.

How to Use the Polynomial Equation Solver Calculator?

The procedure to use the polynomial equation solver calculator is as follows:
Step 1: Enter the polynomial equation in the input field
Step 2: Now click the button “Solve Equation” to get the solution
Step 3: Finally, the solution (Variable value) of a polynomial equation will be displayed in the new window

What is Meant by the Polynomial Equation Solver?

In Mathematics, a polynomial equation is defined as an algebraic equation which has variables, constants, coefficients, and many mathematical operators. A polynomial equation can have many terms with different exponents. The higher exponent value of the polynomial equation is called the degree of an equation. There are different types of polynomial equations, such as Linear polynomial equations, quadratic polynomial equations, cubic polynomial equations, and so on.

A polynomial is defined as a type of expression in which the exponents of the variable should be a whole number.

What is Roots Calculator?

'Roots Calculator' is an online tool that helps to calculate the roots of a given polynomial. Online Roots Calculator helps you to calculate the roots of a given polynomial in a few seconds.

Roots Calculator

NOTE: Enter a polynomial only in terms of x only. 

How to Use Roots Calculator?

Please follow the steps below to find the roots of a given polynomial:

  • Step 1: Enter the polynomial in the given input boxes.
  • Step 2: Click on the "calculate" button to find the roots of a given polynomial. 
  • Step 3: Click on the "Reset" button to clear the fields and solve for different polynomials.

How to Find Roots Calculator?

A polynomial with a degree of 1 is known as a linear polynomial

A polynomial with a degree of 2 is known as a quadratic polynomial.

A polynomial with a degree of 3 is known as a cubic polynomial.

A polynomial with a degree of 4 is known as a quartic polynomial.

A polynomial with a degree of 5 is known as a quintic polynomial.

A polynomial with a degree(n) greater than 5 is known as an nth degree polynomial.

A polynomial with any degree equates it to zero and finds the roots of a given polynomial.

The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2”

An equation of the form ax2 + bx + c = 0, where a ≠ 0 is called a quadratic equation and a, b, c are coefficients of the quadratic equation.

To solve the quadratic equation, we need to find the roots of a given quadratic equation, we use the discriminant formula  given by:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

Finding polynomial equation with roots given calculator

Want to find complex math solutions within seconds?

Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps.

Book a Free Trial Class

Solved Examples on Roots Calculator

  1. Example1:
    Solve the given linear equation 3x + 5 = 0
    Solution:
    3x + 5 = 0
    3x = -5
    x = -5 / 3

  2. Example2:

    Solve the quadratic equation x2 + 5x + 6 =0

    Solution:

    Given: a = 1, b = 5, c = 6

    \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

    \(x = {-5 \pm \sqrt{5^2-24} \over 2}\)

    \(x = {-4 \over 2}, {-6 \over 2}\)

    \(x= {-2},{-3}\)

  3. Example3:
    Find roots of given polynomial x3 - 27 = 0
    Solution:
    x3 - 27 = 0 
    x3 = 27
    x = 3

Show solution >

go to slidego to slidego to slide

Similarly, you can try the calculator to find the roots for the following: 

  • 2x3 + x - 3 = 0
  • x4 + 10x3 - 5x - 11 = 0
  • Polynomials
  • Linear equations
  • Quadratic equations

☛ Math Calculators: