Let for f(x)= a_0 x^2+ a_1 x+ a_2, f^′(0)=1 and f^′(1)=0. If a_0, a_1, a_2 are in an arithmatico-geometric progression, whose corresponding A.P. has…

Let for $\displaystyle f(x)=\mathrm{a}_0 x^2+\mathrm{a}_1 x+\mathrm{a}_2, f^{\prime}(0)=1$ and $\displaystyle f^{\prime}(1)=0$. If $\displaystyle \mathrm{a}_0, \mathrm{a}_1, \mathrm{a}_2$ are in an arithmatico-geometric progression, whose corresponding A.P. has common difference $\displaystyle 1$ and corresponding G.P. has common ratio $\displaystyle 2$ , then $\displaystyle f(4)$ is equal to \_\_\_\_.