1955 AHSME Problem 30

Each of the equations 3x^2-2=25, (2x-1)^2=(x-1)^2, \sqrt{x^2-7}=\sqrt{x-1} has:

\begin{array}{l} \textbf{(A)}\ \text{two integral roots}\qquad\textbf{(B)}\ \text{no root greater than 3}\qquad\textbf{(C)}\ \text{no root zero}\\ \textbf{(D)}\ \text{only one root}\qquad\textbf{(E)}\ \text{one negative root and one positive root} \end{array}

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