1959 AHSME Problem 38

If 4x+\sqrt{2x}=1, then x: \textbf{(A)}\ \text{is an integer} \qquad\textbf{(B)}\ \text{is fractional}\qquad\textbf{(C)}\ \text{is irrational}\qquad\textbf{(D)}\ \text{is imaginary}\qquad\textbf{(E)}\ \text{may have two different values}

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