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(x+a)(x+b)(x+c)(x+d) = x^4+4px^3+6x^2+4qx+1 (HOMC 2013 Q11)

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August 1, 2019
polynomialminimummaximum

Problem Statement

The positive numbers a,b,c,d,p,qa, b,c, d, p, q are such that (x+a)(x+b)(x+c)(x+d)=x4+4px3+6x2+4qx+1(x+a)(x+b)(x+c)(x+d) = x^4+4px^3+6x^2+4qx+1 holds for all real numbers xx. Find the smallest value of pp or the largest value of qq.
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