Question

why the value of distance of the object always negative in the mirror

Answer 1

According to the sign conventions that are followed in Optics, distances to the left of the optical center of the lens are taken as negative and that to the right positive ( you can compare this logic with number line).

For the ease of understanding, another convention that is accepted universally is to always put the object to the left of the lens ( let it be concave or convex or the combination of the both etc.) so that the image is always formed to the right of the lens.

Hence, during calculations we put the negative value of the object distance in the formulae.

Answer 2

because according to sign convention distance is always measured from pole which is opposite to the direction of incident ray.
Hence distance of the object always negative in the mirror.

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