Question

Determine the zeros of f(x) = x3 – 12x2 + 28x – 9.

Answer 1

at least this one has a 9, which does not have a zillion factors

Answer 2

yeah

Answer 3

1st step try +-1 ,+-3 ,+-9

Answer 4

@phi I got up to x^2-3x=-1 after synthetic division... Now I'm lost

Answer 5

x^2 -3x+1=0

that does not factor into nice numbers. do you know the quadratic formula ?

Answer 6

yeah

Answer 7

I got (3+/-√5)/2

Answer 8

@phi I think I'm wrong

Answer 9

that is correct. If you are sure you have the correct equation (no typos) then those are the roots:

9, \(\frac{3+\sqrt{5}}{2} \), \(\frac{3-\sqrt{5}}{2} \)
you can use a calculator and test them

Answer 10

okay

Answer 11

How do you do it if it's a quartic equation and not a cubic?

Answer 12

you can still use the rational root theorem. But in the real world, we would use a computer and "root finding algorithms"

http://en.wikipedia.org/wiki/Root-finding_algorithm