ANSWER
One real root.
EXPLANATION
The graph of the function

is shown in the attachment.
According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.
The x-intercepts gives the number of real roots.
Observe that the graph has only one intercept.
This implies that, the equation:

has only one real solution.
Answer:
a) we know that this is convergent.
b) we know that this might not converge.
Step-by-step explanation:
Given the
is convergent
Therefore,
(a)
The power series
has radius of convergence at least as big as 8. So we definitely know it converges for all x satisfying -8<x≤8. In particular for x = -3
∴
is convergent.
(b)
-8 could be right on the edge of the interval of convergence, and so might not converge