find the roots of
f(x)=x^4-6x^3-10x^2+2x-15

Question

anonymous · Answer

i have the same problem

anonymous · Answer

there are 4 roots in this

anonymous · Answer

x ~~ -1.9134607252052312
x ~~ 7.3594940468468407
x ~~ 0.27698333917919524-0.99421429099634553 i
x ~~ 0.27698333917919524+0.99421429099634553 i
are the four roots, and th elast two are imaginary, ( the reason i've typed an 'i' there)

amistre64 · Answer

there are ways you can improve your odds when searching for roots; I forget the names they give to them, but, it has something to do with the number of times the signs switch; and factors and fractions of first/last....

amistre64 · Answer

1,3,5,15
-1,-3,-5,-15

then use synthetic division to weed them out if possible :)

anonymous · Answer

yes u r right, amistre

anonymous · Answer

the highest power x has , is the no. of roots u get

amistre64 · Answer

the number of "possible" roots, yes.... but we can have no roots as well :)

anonymous · Answer

no roots at all ? not even imaginary ??

amistre64 · Answer

"we dont need no stinkin' toots" - anonymous

take x^2 +5 for example, .... ro :real" roots :)

amistre64 · Answer

urg!!....roots lol

anonymous · Answer

hmmm

amistre64 · Answer

i feel like i have an iphone doing atuo correct on me lol

anonymous · Answer

ha ha h a

anonymous · Answer

Refer to the attachment, jeremy.pdf

The two real roots are clearly visible.  Thinker has them nailed.
The root 7.35.. yields a function value very close to zero. 
$$f(7.35949) = 1.13687 * 10^{-13}$$
By eye ball, one can see where the three derivatives are zero and the two inflection points.

P.S.
If everyone had access to a copy of Mathematica V8, I would venture to guess that there would be very few problems posted to this site.

I have no financial connections to Wolfram.