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Quartic Non-Real Roots Coefficient

2050SpecialistPolynomialsComplex Numbers

AIME · 1995 · Problem 5

For certain real values of $a, b, c,$ and $d_{},$ the equation $x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $13+i$ and the sum of the other two roots is $3+4i,$ where $i=\sqrt{-1}.$ Find $b.$
0 students attempted0% solvedRating 2050

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