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2013 AMC 10BProblem 19P16-20~6 minPrint
QuadraticsSequences & SeriesApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

The real numbers c,b,ac,b,a form an arithmetic sequence with a≥b≥c≥0a\ge b\ge c\ge 0 . The quadratic ax2+bx+cax^2+bx+c has exactly one root. What is this root?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.