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.

Discriminant of a Polynomial - dCode

Tag(s) : Arithmetics,Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

This page is using the new English version of dCode, *please make comments* !

Sponsored ads

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.

For a quadratic polynomial, the discriminant named delta is calculated like this:

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

The fact of knowing the value of the discriminant then solves the equation.

For the equation \( 2x^2+3x+1 = 0 \) of type \( ax^2+bx+c \) you have \( \Delta = b^2-4ac = 3^2-4*2*1 = 1 \)

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

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

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

for the equation \( 2x^2+3x+1 = 0 \) you have \( \Delta = 1 \) so \( x_1 = -1/2 \) 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 complex 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.

dCode retains ownership of the source code of the script Discriminant of a Polynomial. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Discriminant of a Polynomial script for offline use, for you, your company or association, see you on contact page !

discriminant,polynomial,delta,root,quadratic,equation

Source : http://www.dcode.fr/polynomial-discriminant

© 2017 dCode — The ultimate 'toolkit' website to solve every problem. dCode