Solve (x)^4 – 4(x)^3 + 5(x)^2 – 4(x) + 1 = 0 in the complex field.?

Question

after solving it in the complex field, it also needs to be factorised in the real and rational fields.

thanks in advance =)

it doesn't have any rational roots, but what about complex and real?

Answer 1

Let p(x) = x^4 - 4x^3 + 5x^2 - 4x + 1

In order for us to factorize this, we need to find the roots of the equation. What we look at are the factors of the constant term (the one without an x, which, in our case, is the 1), and TEST factors of 1 to see if p(x) is equal to 0. That is, we want to test
p(1) and p(-1)

p(1) = 1 - 4 + 5 - 4 + 1 = -3 + 1 + 1 = -1, which is non-zero
p(-1) = 1 + 4 + 5 + 4 + 1 = [something non-zero]

For that reason, there are no rational roots.

Answer 2

if you didn't undertand a thing in school, thats why you have a teacher!...no offense dude

Answer 3

Dude, get a life!!!

Answer 4

do your own homework you self u big cheater!