We present sharp lower bounds for the A-numerical radius of semi-Hilbertian space operators. We also present an upper bound. Further we compute new upper bounds for the B-numerical radius of 2 × 2 operator matrices where B= diag(A, A) , A being a positive operator. As an application of the A-numerical radius inequalities, we obtain a bound for the zeros of a polynomial which is quite a bit improvement of some famous existing bounds for the zeros of polynomials.