quadradics with 4 answers: x^4-5x^2+4=0

[fresh83]

ummmm im doing some problems and i came across the equation x^4-5x^2+4=0

i know its going to have 4 answers ....but i dont remember how or how to get 4 answers ...the way im doing it is only turning up 2

 

[fresh83]

Re: quadradics with 4 answers

and after making this thread im remembering something about setting x^2 = w .


just letting everyone know what i know or....dont .

 

[Loren]

Re: quadradics with 4 answers

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

(x^2-1)(x^2-4)=0

Now set each of these factors equal to 0 and solve for x. You should get 2 roots for each for a total of 4 roots.

As a reminder... Solve x^2-9=0
Two ways.

x^2-9=0
x^2=9
\(\displaystyle \sqrt{x^2}=\pm \sqrt{9}\)
\(\displaystyle x=\pm 3\)

Second way.

x^2-9=0
(x+3)(x-3)=0
x+3=0 or x-3=0
x=-3, x=3.