Question

Find the roots of the polynomial equation x^4 - 5x^3 + 11x^2 - 25x + 30

Answer 1

Using the remainder theorem f(2) = 2^4 - 5^3 + 11^2 -25x2 + 30 = 0

then (x - 2) is a factor 1st root is at x = 2

using polynomial division (x -2)(x^3 -3x^2 +5x -15) = x^4 - 5x^3 +11x^2 - 25x + 30

look at (x^3 - 3x^2 + 5x -15) and the remainder theorem f(3) = 0 then (x - 3) ix a factor

using division gives Q(x) x^2 + 5

then \[x^4 - 5x^3 + 11x^2 - 25x + 30 = (x-2)(x-3)(x^2+5)\]

which gives the roots \[x = 2, 3, \pm \sqrt{5} i\]

Answer 2

Omgee thank you so very much! I'm doing online schooling and have been trying to figure it out for the past couple hours. Thanks Muchiies. :)

Answer 3

And the lessons dont really show you how to do it.

Answer 4

well I just start with guess and check to find the 1st root... stating at 1 or -1, 2 or -2 you normally have a factor by the time you get to 3

Answer 5

hAHAHA okay. Thanks a lot though :)