find roots of f(x) = (1 - 3x^2) / (x^3 - x)^2

[calculusIsKillingMe]

I'm having trouble with finding the roots for f(x).

f(x) = (1 - 3x^2) / (x^3 - x)^2

 

[stapel]

I'm having trouble with finding the roots for f(x).

f(x) = (1 - 3x^2) / (x^3 - x)^2

Use what you learned back in algebra. The roots are the zeros, so set this equal to zero, and solve the resulting quadratic.

 

[calculusIsKillingMe]

I tried to do that and got root 1 over 3. I know the right answer is root 3 over 3. but I dont know how to get it

 

[stapel]

I tried to do that and got root 1 over 3. I know the right answer is root 3 over 3. but I dont know how to get it

Unfortunately, it is not possible to trouble-shoot work which has not been posted.

Please reply showing your steps so far, so we can see where things are going sideways. Thank you!

 

[ksdhart]

I tried to do that and got root 1 over 3. I know the right answer is root 3 over 3. but I dont know how to get it

Well, if I'm reading your post correctly, then this is answer you got:

\(\displaystyle \sqrt{\frac{1}{3}}\)

And your book has this answer:

\(\displaystyle \frac{\sqrt{3}}{3}\)

If that's the case, then the answers are, in fact, the same. By the properties of square roots, you can write your answer as:

\(\displaystyle \frac{\sqrt{1}}{\sqrt{3}}\)

Now what happens if you multiply both the numerator and the denominator by square root of 3, to clear the square root from the denominator?

 

[calculusIsKillingMe]

Oh I see now, thanks for the help