z^4+z^3+z^2+z+1=0

3 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to multiply both sides by `z - 1`  such that:

`(z-1)(z^4+z^3+z^2+z+1) = 0*(z-1)`

You need to convert the product to the left side into a difference of powers such that:

`z^5 - 1 = 0 => z^5 = 1 => z^5 = root(5)1 => z = 1`

Since the graph below representing the function `f(x)=x^4+x^3+x^2+x+1` , does not intercept x axis, hence, the equation has no real roots but 4 complex roots.

mfds's profile pic

mfds | eNotes Newbie

Posted on

huhlhon;kn;k

We’ve answered 318,982 questions. We can answer yours, too.

Ask a question