ANSWER
The root at point P may be [tex] \frac{3}{5} [/tex]
EXPLANATION
The given function is
[tex]f(x) = 5 {x}^{5} + \frac{16}{5} x - 3[/tex]
The potential rational roots are all factors of -3 expressed over all factors of 5.
These are:
[tex] \pm \frac{1}{5} , \pm \frac{3}{5} [/tex]
Since the root of f(x) at P is closer to 1 that zero and it is positive , that potential may be [tex] \frac{3}{5} [/tex]
