Search for a tool
Discriminant of a Polynomial

Tool to compute the discriminant of a polynomial. A discriminant of a polynomial is an expression giving information about the nature of the roots of the polynomial.

Results

Discriminant of a Polynomial -

Tag(s) : Functions

Share
Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developped the best Discriminant of a Polynomial tool, so feel free to write! Thank you !

Discriminant of a Polynomial

Discriminant Calculator



Tool to compute the discriminant of a polynomial. A discriminant of a polynomial is an expression giving information about the nature of the roots of the polynomial.

Answers to Questions

How to calculate a discriminant?

For a quadratic polynomial $ ax^2+bx+c $, the discriminant named delta $ \Delta $ is calculated with the formula:

$$ \Delta = b^2-4ac $$

The fact of knowing the value of the discriminant then solves the equation more easily through formulas (using this discriminant).

Example: The equation $ 2x^2+3x+1 = 0 $ of type $ ax^2+bx+c $ (with $ a = 2 $, $ b = 3 $ et $ c = 1 $) has for discriminant $ \Delta = b^2-4ac = 3^2-4*2*1 = 1 $

For a cubic polynomial of the form $ ax^3+bx^2+cx+d $ the discriminant formula is

$$ \Delta = b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd $$

For a polynomial of degree 1 or 0 the determinant is not generally calculated, its value has no interest.

How to find the roots of a polynomial with the determinant?

For a quadratic polynomial of type $ ax^2+bx+c = 0 $

If the discriminant is positive (strictly), the equation has two solutions:

$$ x_1 = \frac {-b + \sqrt \Delta}{2a} \\ x_2 = \frac {-b - \sqrt \Delta}{2a} $$

Example: The equation $ 2x^2+3x+1 = 0 $ has for discriminant $ \Delta = 1 $, so solutions are $ x_1 = -1/2 $ and $ x_2 = -1 $

If the discriminant is zero, the equation has a double root:

$$ x_1=x_2 = -\frac b{2a} $$

If the discriminant is negative (strictly), the equation has 2 complex conjugate solutions:

$$ \delta^2 = \Delta $$

$$ x_1 = \frac {-b + \delta}{2a} \\ x_2 = \frac {-b - \delta}{2a} $$

For equations of higher degrees, the calculations are much more complicated, but knowledge of the determinants is important.

Source code

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

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Discriminant of a Polynomial tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/polynomial-discriminant
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback