Solve this quintic equation:
Note: You don't have to find the roots. Just show us how to find them!
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
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
yeah.this problom was solved over 300 years ago by some mathematician!
Quintic Equation -- from Wolfram MathWorld