Find the remaining roots of: x^3+2x^2-5x-6=0, root x=-1
Favorites|Homepage
Subscriptions | sitemap
HOME > > Find the remaining roots of: x^3+2x^2-5x-6=0, root x=-1

Find the remaining roots of: x^3+2x^2-5x-6=0, root x=-1

[From: ] [author: ] [Date: 11-11-28] [Hit: ]
2. .-5 . .-6. ___-1_-1___6_.......
Hi,

Given x³ + 2x² - 5x - 6 = 0, and x = -1 is a root, find the others.
. ____________
-1)1 . 2. .-5 . .-6
. ___-1_-1___6_
. . 1 . 1 -6 . . 0

1 . 1 -6 are the quadratic x² + x - 6 which factors into (x + 3)(x - 2) = 0.

These solve to x = -3 and x = 2.



The roots are x = -3, x = -1, and x = 2. <==ANSWER

I hope that helps!! :-)

-
note that highest power x-term is 3 so there are three solutions in form
(x-x1)(x-x2)(x-x3) where x is variable x, and x1,x2, x3 are solutions

in your case you know that x1=-1 so above factored form is then
(x-(-1))(x-x2)(x-x3)
(x+1)(x-x2)(x-x3)

to find remaining two terms we just do polynomial division
(x^3+2x^2-5x-6) / (x+1) = x^2+x-6

and that can be factored as (x-2)(x+3)

which brings last two solutions:
x2=2
x3=-3

-
Two ways of doing this.

The best is to see that as x=-1 is a solution, then (x+1) is a factor. Divide x^3+2x^2-5x-6 by x+1 (see http://en.wikipedia.org/wiki/Polynomial_…
To give x^2 + x - 6 which factorises to (x+3)(x-2), so the other roots are -3 and 2.

The other method is to try other integers, and when you try x=-3 and x=2, the expression will equal 0. So you know (x+3) and (x-2) are factors. This can waste time or save time, depending on whether the other factors are integers, normally they won't be.

-
x ^ 2 + x - 6 [After synthetic division]

(x + 3 ) ( x - 2 )

x = -3 , x = 2
1
keywords: remaining,the,roots,root,of,Find,Find the remaining roots of: x^3+2x^2-5x-6=0, root x=-1
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .