1984 AHSME Problem 24

If a and b are positive real numbers and each of the equations x^2+ax+2b=0 and x^2+2bx+a=0 has real roots, then the smallest possible value of a+b is

\mathrm{(A) \ }2 \qquad \mathrm{(B) \ }3 \qquad \mathrm{(C) \ } 4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ } 6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.