Solve this quintic equation:

Note: You don't have to find the roots. Just show us how to find them! (Evilgrin)

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- August 28th 2009, 10:27 AMNonCommAlgA quintic equation!
Solve this quintic equation:

__Note__: You don't have to find the roots. Just show us how to find them! (Evilgrin) - August 29th 2009, 12:21 AMsimplependulum
Let me try it !

The next step is substituting , is a constant

Let

then let's see what the coefficient of is

Which equals to that in the equation

and finally compare the remaining coefficient :

we will see that so that we can obtain the values of , the root are - August 29th 2009, 12:42 AMsimplependulum
Here is another method :

We have or

Sub.

Again , let

we will obtain

and let

Let

we will find

and

we know are the roots of the quadratic equation

After finding them , the roots of the quintic equation can also be found .

For example , let

which satisfies - August 29th 2009, 12:03 PMNonCommAlg
probably an easier way is to just substitute

this problom was solved over 300 years ago by some mathematician! (Surprised) - August 29th 2009, 03:15 PMluoboQuote:

this problom was solved over 300 years ago by some mathematician! (Surprised)

Quintic Equation -- from Wolfram MathWorld