Find the x intercepts of 3x^4 - 6x^2 + (5/3)

Re: Find the x intercepts



Hello M Hunt:

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Find the x intercepts of

3x^4-6x^2+(5/3)

I know that in order to get my x intercepts i need to factor this equation, but i am not sure how to factor it when it is to the 4th order. I also know that i will have four answers because it is to the fourth order. Is it possible to factor it out to somethign like (3x^2-6x)^2. I am not sure if that is legal to do, and if i do it i am not sure what would happen to the 5/3. Please help!!! thank you :D
 
Re: Find x intercepts

Find the x intercepts of

3x^4-6x^2+(5/3)

I know that in order to get my x intercepts i need to factor this equation, but i am not sure how to factor it when it is to the 4th order. I also know that i will have four answers because it is to the fourth order. Is it possible to factor it out to somethign like (3x^2-6x)^2. I am not sure if that is legal to do, and if i do it i am not sure what would happen to the 5/3.
Click to expand...

Your thoughts are headed in the right direction. First multiply by 3 to get rid of the fraction:

9x^4 – 18x^2 + 5 = 0

Now factor it:

(_x^2 - _)(_x^2 - _) = 0

And solve.
 
I would do a substitution first:

u = x^2

3u^2 - 6u + 5/3 = (3u - 1)(u - 5/3) .........now back substitute u = x^2
 
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