# Quadratic Equations and Substituting "Appropriately?"

• Dec 7th 2011, 10:15 AM
annon25
I have a section in my book that is asking me to "make an appropriate substitution" for a set of problems; and the book doesn't even give examples on how to do this sort of thing.

Here is one for example:

x^4-5x^2+4=0

Help, anyone?

Thanks
• Dec 7th 2011, 10:21 AM
Quacky
Re: Quadratic Equations and Substituting "Appropriately?"
Let $x^2=k$
• Dec 7th 2011, 10:30 AM
TheChaz
Re: Quadratic Equations and Substituting "Appropriately?"
Quote:

Originally Posted by annon25
I have a section in my book that is asking me to "make an appropriate substitution" for a set of problems; and the book doesn't even give examples on how to do this sort of thing.

Here is one for example:

x^4-5x^2+4=0

Help, anyone?

Thanks

They want you to make a substitution (let's use "k", as Quacky suggests) so that your equation can be written as
ak^2 + bk + c = 0.

With k = x^2, we have
k^2 - 5k + 4 = 0
(k .... )(k ....) = 0
etc.