Question 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 $b.$
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 $b.$