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Clever Vieta Manipulation

Source: 1971 AHSME Problem 20

April 20, 2014
algebrapolynomialVietaabsolute valueAMC

Problem Statement

The sum of the squares of the roots of the equation x2+2hx=3x^2+2hx=3 is 1010. The absolute value of hh is equal to
<spanclass=′latex−bold′>(A)</span>−1<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>32<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>None of these<span class='latex-bold'>(A) </span>-1\qquad<span class='latex-bold'>(B) </span>\textstyle\frac{1}{2}\qquad<span class='latex-bold'>(C) </span>\textstyle\frac{3}{2}\qquad<span class='latex-bold'>(D) </span>2\qquad <span class='latex-bold'>(E) </span>\text{None of these}
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