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Polynomial Root

Tool to calculate/find the root of a polynomial. In mathematics, a root of a polynomial is a value for which the polynomial is 0. A polynomial of degree n can have between 0 and n roots.

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Polynomial Root -

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Polynomial Root

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Answers to Questions (FAQ)

How to calculate a polynomial root?

The general principle of root calculation is to evaluate the solutions of the equation polynomial = 0 according to the studied variable (where the curve crosses the y=0 zero axis)..

Example: Determinate the roots of the quadradic polynomial $ ax ^ 2 + bx + c $, they are the solutions of the equation $ ax ^ 2 + bx + c = 0 $ so $$ x = \frac{ \pm \sqrt{ b ^ 2-4ac } -b}{2 a} $$

The calculation of polynomial roots generally involves the calculation of its discriminant.

Example: For a quadratic polynomial $ ax ^ 2 + bx + c $ the discriminant is $ \Delta = b ^ 2-4 a c $

How to calculate a discriminant?

Use the polynomial discriminant calculator on dCode which automatically adapts to polynomials of degree 2, degree 3, etc. degree n.

How to find trivial roots?

An trivial root is an easily spotted polynomial root. Either because it is the simplest roots like 0, 1, -1, 2 or -2, or because the root is deductible by simply looking at the polynomial.

Example: The polynomial $ (x+3)^2 $ has $ -3 $ as trivial/obvious root

What is a zero for a polynomial?

A zero of a polynomial function $ P $ is a solution $ x $ such that $ P(x) = 0 $, so it is the other name of a root.

What is a nt degree polynomial?

The order of a polynomial (2nd order 2 or quadratic, 3rd order or cubic, 4th order, etc.) is the value of its largest exponent.

Example: $ x^3+x^2+x $ is a polynomial of 3rd order

How to find a polynomial with given roots/zeros?

A polynomial having $ n $ roots / zeros noted $ x_1, x_2, \ cdots, x_n $ is a polynomial of degree $ n $ which can be written in the form: $$ P (x) = (x-x_1)(x-x_2) ... (x-x_n) $$

Example: Find a polynomial having the following roots: $ 1 $ and $ -2 $, answer is written $ P(x) = (x-1)(x+2) $

Sometimes the roots are the same, or the degree is known but there is only one root, then this one is repeated.

Example: Find a polynomial of degree 2 having for unique root $ 1 $, answer is $ P(x) = (x-1)(x-1) = (x-1)^2 = x^2 − 2x + 1 $

What is the sum of the roots of a 2nd degree polynomial?

The sum of the real roots of a polynomial of degree 2 is $ -\frac{b}{a} $

What is the product of the roots of a 2nd degree polynomial?

The product of the real roots of a polynomial of degree 2 is $ \frac{c}{a} $

Source code

dCode retains ownership of the online 'Polynomial Root' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Polynomial Root' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Polynomial Root' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Polynomial Root' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

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Thanks to your feedback and relevant comments, dCode has developed the best 'Polynomial Root' tool, so feel free to write! Thank you!


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