Question

I'm struggling to find the zeros of 48x^3-80x^2+41x-6

Answer 1

Do you know how to use synthetic division? And do you know about rational zeros? Do you know anything about Descartes' rule of signs for real solutions? Any of the above?

Answer 2

I know the process of doing it. I just cant find the divisor

Answer 3

I feel like I've tried everything and I cannot get the remainder to = 0

Answer 4

with the factors of 48 and -6

Answer 5

From the sign changes, there is at least one real positive zero which may or may not be rational. To see if it is rational, you have to try all combinations of divisors of -6 over divisors of 48. Just got your last comment so it appears you know this. So, just start trying them.

Answer 6

There are around 20 or so candidates and I know that number is daunting, but the odds are that you'll find it within 7-8 tries. It's just trial-and-error at this point and you just have to try them all. It's a brute force problem. No easy way to get to where you want to get to.

Answer 7

+1 or -1, +2 or-2, +3 or-3,+4or-4, +6or-6, +8or-8, +12or-12, +16or-16, +24or-24, +48or-48/+1or-1, +2or-2, +3or-3, +6or-6

Answer 8

Those are my combinations correct

Answer 9

rational roots theorem is factors plus/minus 6/48 ie 1/8

Answer 10

ie plus/minus 1,!/2, 1/4,!/8

Answer 11

Attached is a plot of \[48 x^3-80 x^2+41 x-6 \]between x=0.2 and x=0.8 .
Also
\[48 x^3-80 x^2+41 x-6=(3 x-2) (4 x-3) (4 x-1) \]

Answer 12

I'm confused...this entire time I have done it so where it would be the factors of 48/6...not the factors of 6/48...and up until now it was working every time

Answer 13

Well, often the lower factors might be the same either way.

This time the coefficient is large though...

Answer 14

http://en.wikipedia.org/wiki/Rational_roots_theorem

Answer 15

I see where I messed up...

Answer 16

I'll probably be banned from this site for this one.

http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html

Answer 17

If only this was how everyone thought haha

Answer 18

@ChrisP80

Attached is an example of a one line computer statement solving a calculus problem using the Mathematica program.

Answer 19

Sorry, there are some words misspelled in the computersolution.pdf .

Answer 20

As usual, the truth is likely somewhere in between all the tech ra ra and the pencil and paper brigade.

I definitely think technology has a role to play, it's not yet entirely clear how to fit it into education in a sensible way (more especially when there is a significant amount of resistance)

Answer 21

@estudier

Thank you for your thought.