Question

why does the image of a red rose look red where as its shadow is black

Answer 1

There are several reason. You should put a link to a real image in the comments, to have specific reasons.

I assume you are speaking about a photo. Many cameras are not so good on dynamic range, so the dark parts tend to be rendered as black. Additionally, automatic exposition put the image luminous like an average grey. So petals tends also not to be much bright. Lots of information is lost.

The real colour of shadows tend to be darker (less/no direct illumination) and unsaturated (indirect light, arriving also from background/wall (neutral) objects. Really some part of the shadow will be neutral colour: the reflected light (from rose) will not reflect on background (shadow) toward your eyes.

Answer 2

The image of red rose look red because red rose reflects only red light rays which fall on it due to which the reflected red light once again gets reflected when it falls on mirror.