Question

What are the roots of (8sqrt3)h^3-512h^2+1024h-512=0

Answer 1

What's your plan for finding them? With degree 3, there must be at least one (1) Real.

Answer 2

It's an equation I got from solving the height of some hexagonal vase in the book. I placed it in wolfram and got the correct answer but I have no Idea how to get the roots.

Answer 3

Since it is cubic, there IS a way, but you probably don't want to know it. You probably should pursue numerical methods. Evaluate the polynomial until you find where it is zero.

Answer 4

Maybe I should've asked for what method to use, I don't think I can group it nor is it feasible to use synthetic division on.

Answer 5

you could try finding f(0), f(1) and f(2) to find location of a root
this is a numerical method

Answer 6

Why not? Use what you have. Who cares if it seems feasible?! Fire up a spreadsheet. It doesn't care if there are lots of decimal places.

You're in luck. There are three positive real solutions. Perhaps the physical reality of the vase suggests that the one around h = 35 is more appropriate than the two around h = 1?

Answer 7

Woah, first I'll have to research how to make a spreadsheet. Anyway, if I am to use a spreadsheet then I already know the answer. 34.88, straight from the book.

Answer 8

Thank you for the help.

Answer 9

mpj4 - do you have a spreadsheet program?

Answer 10

I don't think I do. Lemme see.

Answer 11

If you don't there's one for free at Open Office

Answer 12

I'll get a link if you want

Answer 13

That would be great.

Answer 14

okay wait a second

Answer 15

Go here:
http://www.openoffice.org/download/index.html
It is great - I use it myself. Microsoft called something like this Microsoft Office and it cost a few hundred bucks. This is free !!!

Answer 16

Ah, thank you. If I find it useful I'll pirate software.

Answer 17

Well, I know it's bad but... meh.

Answer 18

It's actually legitimate. I believe the company called Oracle put their own version out for free! Nice to see corporate America doing something good!

Answer 19

Haha, alright, I appreciate the goodwill. I'll be sure to use this.

Answer 20

Okay - I highly recommend it and I suggest it to just about anyone I can.

Answer 21

Okay - gotta go - cya mpj4