1995 AIME Problems/Problem 5

Problem

For certain real values of $\displaystyle a, b, c,$ and $\displaystyle d,$ the equation $\displaystyle x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $\displaystyle 13+i$ and the sum of the other two roots is $\displaystyle 3+4i,$ where $i=\sqrt{-1}.$ Find $\displaystyle b.$

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1995 AIME Problems/Problem 5

Problem

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