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2005 AMC 10BProblem 16P16-20~3 minPrint
QuadraticsAlgebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

The quadratic equation x2+mx+nx^2+mx+n has roots twice those of x2+px+mx^2+px+m , and none of m,n,m,n, and pp is zero. What is the value of n/pn/p ?

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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. Also appeared as 2005 12B #12.