AGE... (Again!)

[bristy1588]

Shokal and Shishir were talking about their ages.
Shokal said, "My age is the root of a polynimial".
After seeing the polynomial $P(n)$, Shishir told, "Your Age is $7$ years".
Then again Shishir told"Oh, I have made a mistake. Actually $P(7)$=77."
Shokal told, "Yes, My age is much more than that".
Shishir came up with another number, $k$, and after telling that he understood that he was wrong, as $P(k)=85$. Find Shokal's age.

[*Mahi*]

Shokal and Shishir were talking about their ages.
Shokal said, "My age is the root of a polynimial".
After seeing the polynomial $P(n)$, Shishir told, "Your Age is $7$ years".
Then again Shishir told"Oh, I have made a mistake. Actually $P(7)$=77."
Shokal told, "Yes, My age is much more than that".
Shishir came up with another number, $k$, and after telling that he understood that he was wrong, as $P(k)=85$. Find Shokal's age.

First of all, $P(n)$ is a polynomial makes no sense if its not with integer coefficients. Only when all the coefficients are integer, there will be valid answer.
So, hint:

For any polynomial $F:\mathbb N \rightarrow \mathbb N , a-b|F(a)-F(b)$

This reduces the problem to

$k-7 |14 , 7-x|77 , k-x|85$ where $x$ is Shokal's age.