# 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

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

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]}