To solve this problem you need to use two equations.
The first is the equation for Magnification which is:
M = -q / p
and the second equation is the mirrior equation which is:
1/p + 1/q = 2/R
R is the radius of curvature, and q is the image distance.
First step is to solve for q, which is:
q = -M*p
Next, you can plug p and q into the mirror equation and solve for R.
R = 2/ (1/p + 1/q)
**note R is positive