algebra, polynomial, discriminant

Reek · 2011-10-02 07:06:06

How can we derive the formula that calculates the discriminant of a polynomial?
Could anyone please explain the process to me? I'm in a hurry, please do make it quickly.
(I am saying about a polynomial in x over the set of complex numbers.)

Level of mine:University level

Last edited by Reek (2011-10-02 22:25:17)

bobbym · 2011-10-02 07:44:46

Hi Reek;

There is no simple way after a quadratic. The classical way uses determinants. These are known to be large and slow.

That is the discriminant of the general cubic:

As you can see it is quite large.

When you have time look here.

http://en.wikipedia.org/wiki/Discriminant

Reek · 2011-10-02 21:19:48

Thank u bobbym for your assistance.

bobbym · 2011-10-02 22:38:19

Hi Reek;

Your welcome. If you have a particular one or type I would run it off for you.

The good news is that you rarely need it. Sometimes you will use it for theoretical ideas but for the character of most of the roots there are easier ways.

Reek · 2011-10-04 05:40:48

Hello Bobbym;

here are the particulars

−2x^3 − 15x^2 − 6x + 7 = 0

2x^4 − 11x^3 − 6x^2 + 64x + 32 = 0

Last edited by Reek (2011-10-04 05:48:11)

bobbym · 2011-10-04 06:29:45

Hi Reek;

The first one is

Next one is

Math Is Fun Forum

#1 2011-10-02 07:06:06

algebra, polynomial, discriminant

#2 2011-10-02 07:44:46

Re: algebra, polynomial, discriminant

#3 2011-10-02 21:19:48

Re: algebra, polynomial, discriminant

#4 2011-10-02 22:38:19

Re: algebra, polynomial, discriminant

#5 2011-10-04 05:40:48

Re: algebra, polynomial, discriminant

#6 2011-10-04 06:29:45

Re: algebra, polynomial, discriminant

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