A convex mirror always produces a virtual image of real object independent of the location of the object use mirror equation to peove it.

Explanation

From mirror formula
`(1)/(v)+(1)/(u)=(1)/(f) rArr(1)/(v)=(1)/(f)-(1)/(u)`
For convex mirror,
Object distance `u` is negative and the focal length `f` is positive.
`therefore (1)/(v)=(1)/(+f)-(1)/(-u)=(1)/(f)+(1)/(u)`
Therefore, the image distance is always positive incase of a convesx mirror.
Hence, the convex mirror always formed a virtual image.