1959 AHSME Problem 34

Let the roots of x^2-3x+1=0 be r and s. Then the expression r^2 + s^2 is: \textbf{(A)}\ \text{a positive integer} \qquad\textbf{(B)}\ \text{a positive fraction greater than 1}\qquad\textbf{(C)}\ \text{a positive fraction less than 1}\qquad\textbf{(D)}\ \text{an irrational number}\qquad\textbf{(E)}\ \text{an imaginary number}

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