# Stuck with this cubic equation

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1. Feb 12, 2017

### Ameer Bux

1. The problem statement, all variables and given/known data

2. Relevant equations
Doesn't state

3. The attempt at a solution
Refer to attached image

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• ###### IMG_0741.JPG
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2. Feb 12, 2017

### Buzz Bloom

Hi Ameer:
I also found two values for x for which f'=0, but my values are different than yours. Might you have copied the problem incorrectly?

Regards,
Buzz

3. Feb 12, 2017

### Staff: Mentor

Since the problem is shown as an image, I don't see how it could have been copied incorrectly. I'm wondering if there is a typo in the problem itself. I too get two values for critical points. The only way that there will be only one solution for x in solving for f'(x) = 0, is the the discrimant has to be zero. IOW, $4c^2 - 24m = 0$. If $c^2 = 8m$, the discriminant is $32m - 24m = 8m$.

One comment about the OP's work: if $c^2 = 8m$, then it's not necessarily true that $c = 2\sqrt{2m}$. Corrected, it would be $c = \pm 2\sqrt{2m}$.

4. Feb 12, 2017

### Staff: Mentor

5. Feb 12, 2017

### Ameer Bux

I'm sorry. I'll check your link and won't post it like I did the next time. Thank you

6. Feb 12, 2017

### Ameer Bux

Hi people. I emailed my teacher and he said that : C² = 6M

There was a typing error on the page.

7. Feb 12, 2017

### Ameer Bux

8. Feb 12, 2017

### Ameer Bux

Got it, thanks guys

9. Feb 12, 2017

### Staff: Mentor

It's a lot simpler to NOT substitute for c^2 until later.
If f'(x) = 0, then $x = \frac{2c \pm \sqrt{4c^2 - 24m}}{12}$. Now, replace $c^2$ with 6m.