Let's apply the mirror equation which is:
`1/d_o + 1/d_i=1/f`
where `d_o` ` `- object distance, `d_i` ` `- image distance and `f ` - focal length.
Note that, magnification factor is the ratio of image distance to object distance.
Magnification factor `= ` `-d_i/d_o`
Since magnification factor is +3 and object distance is 30 cm, then
Isolate `d_i` .
Then, substitute `d_o=30` cm and `d_i=-90` cm to the mirror equation.
`1/30 + 1/(-90)=1/f`
To simplify the equation, multiply both sides by the LCD which is 90f.
`90f*(1/30 + 1/(-90))=(1/f) *90f`
Solve for f.
Moreover in curved mirrors, the focal length is half the raduis of the curvature of mirror. So,
`f = R/2`
Substitute value of f.
`45*2 = R`
Hence, the raduis of curvature of the mirror is 90 cm.