1955 AHSME Problems/Problem 27

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If $r$ and $s$ are the roots of $x\^{}2 - px + q = 0$ (Error compiling LaTeX. Unknown error_msg), then $x\^{}2 + s\^{}2$ (Error compiling LaTeX. Unknown error_msg) equals:

$(A) p\^{}2 + 2q$ (Error compiling LaTeX. Unknown error_msg) $(B) p\^{}2 - 2q$ (Error compiling LaTeX. Unknown error_msg) $(C) p\^{}2 + q\^{}2$ (Error compiling LaTeX. Unknown error_msg) $(D) p\^{}2 - q\^{}2$ (Error compiling LaTeX. Unknown error_msg) $(E) p\^{}2$ (Error compiling LaTeX. Unknown error_msg)