# How do you find the number of complex, real and rational roots of #5+x+x^2+x^3+x^4+x^5=0#?

##### 2 Answers

#### Answer:

One real root and two pairs of conjugate complex roots.

#### Explanation:

We have that

includes de roots of

The solution for the real roots of

We know that

Finally the structure for

#### Answer:

My answer is just to locate the only real root that is negative and close to -1.5 and also the point near (0, 5)

#### Explanation:

The real root can be bracketed to the desired sd-accuracy by

iterative methods. The 2-sd approximation is

aspects are very clear, in the nice answer by Cesareo R

graph{5+x+x^2+x^3+x^4+x^5 [-23.11, 4.91, -7.01, 6.99]}