If a and b are positive real numbers and each of the equations x^2+ax+2b = 0 \text{and} x^2+2bx+a = 0 has real roots, then the smallest possible value of a+b is<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>5<spanclass=′latex−bold′>(E)</span>6