if a root of the equation x^3-4x^2+2x+4=0 is equal to the sum of the other two roots, find the roots

Question

anonymous · Answer

to t the sum of the other two roots?

anonymous · Answer

opps sorry, that's a typo

anonymous · Answer

uh i have the three roots

anonymous · Answer

how did you find them?

anonymous · Answer

-.7320508076
2
2.7320508076

anonymous · Answer

hm.. how did you do that?

anonymous · Answer

well i saw that 
(x-2) could be taken out of the first three terms

anonymous · Answer

sorry, I'm not sure how you took it out, did you factorise the x out?

anonymous · Answer

https://www.dpmms.cam.ac.uk/~wtg10/cubic.html

anonymous · Answer

All of the knowledge on solving cubic equations.

anonymous · Answer

aw thanks! But we haven't been taught this yet. Is there another way of doing this question?

anonymous · Answer

Well it gets confusing after cubic equations.. i normally try to find the quadratic equation in there and then take it out. and the rest will factor itself out... but not really 100% sure

anonymous · Answer

I don't know either. I tried making the roots a, b, (a+b), found the product and sum of roots and tried to solve it from there but it wouldn't work

anonymous · Answer

hi duplicity do you know synthetic division? use it here

anonymous · Answer

or just divide the eq by 2 to get
x^3-4x^2+2x+4=0 
(x-2)(x^2-2x-2)=0
now we know the root x1=2 you can find the other two roots by using the quadratic formula

anonymous · Answer

hi mark, how did you divide the eq by 2 to get (x-2)(x^2-2x-2)=0?

anonymous · Answer

im sorry divide by x-2

anonymous · Answer

ah I see! How did you know to divide by that?

anonymous · Answer

i use synthetic division, are you familiar with that?

anonymous · Answer

sorry, nope. but what is it?

anonymous · Answer

it is one of good tool for finding roots of polynomials by first guessing

anonymous · Answer

oh! is it where you sub in factors of the remainder to check if it makes a zero?

anonymous · Answer

yes it is try this one http://en.wikipedia.org/wiki/Synthetic_division

anonymous · Answer

or try this http://mathworld.wolfram.com/SyntheticDivision.html

anonymous · Answer

Ok, I got it! It like another version of polynomial division. Thank you!!

anonymous · Answer

yes it is ..lol
ok yw good luck now