### Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.

**Sage question:**
Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.
Sage code I have found.

K.<c>=QQ['c']

R.<x>=K[]

f=x^2+x+c+1

f

How do I find the code for the $c$ values where $x^2 + x + c + 1$ has a double root. Also, can you give some examples so that I can construct some programming code in sage?