1956 AHSME Problem 23

About the equation ax^2 - 2x\sqrt {2} + c = 0, with a and c real constants, we are told that the discriminant is zero. The roots are necessarily:

\begin{array}{l} \textbf{(A)}\ \text{equal and integral}\qquad \textbf{(B)}\ \text{equal and rational}\qquad \textbf{(C)}\ \text{equal and real} \\ \textbf{(D)}\ \text{equal and irrational} \qquad \textbf{(E)}\ \text{equal and imaginary} \end{array}

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