SOLUTION: We are given a polynomial equation and one or more of its roots. Find the remaining roots. {{{x^4+3x^3-3x^2+3x-4=0}}} Roots are x=-4 and x=1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: We are given a polynomial equation and one or more of its roots. Find the remaining roots. {{{x^4+3x^3-3x^2+3x-4=0}}} Roots are x=-4 and x=1      Log On


   

Question 478860: We are given a polynomial equation and one or more of its roots. Find the remaining roots. x%5E4%2B3x%5E3-3x%5E2%2B3x-4=0 Roots are x=-4 and x=1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Using synthetic division: roots are: 1,-4, i,-i



x^4+3x^3-3x^2 +3x-4)/(x-1) = x^3 + 4x^2 + x + 4



1	1	3	-3	3	-4

		1	4	1	4

	1	4	1	1	0



(x^3 + 4x^2 + x + 4)/(x+4) = x^2+1, x^2+1 = 0 , x = ± i

-4	1	4	1	4

		-4	0	-4

	1	0	1	0