For what value on "a" has the equation an infinite amount of solutions?

For a quadratic polynomial:

What is the polynomial p(x).

I don't want the answers to these questions, I simply would like some help with them. As I don't know where to start with either of them.

EDIT: I believe that I have managed to solve the first problem. I'd like to know if it's a valid solution.

"[unparseable or potentially dangerous latex formula]"

Hopefully this will suffice.

(x^2+2x+1)^2 = (x+a)^4

(x^2+2x+1) = (x+a)^2

(x+1)^2 = (x+a)^2

(x+1) = (x+a)

1 = a