Math (Algebra)
posted by Shin on .
f(x)=x^4+ax^3+bx^2+cx+d and has real coefficients. If two of the roots are 4−i and 2+3i, what is the value of a+b+c+d?

complex roots always come in conjugate pairs. So,
f(x) = (x(4i))(x(4+i))(x(2+3i))(x(23i))
= ((x4)^2 + 1^2)((x2)^2 + 3^2)
= (x^28x+17)(x^24x+13)
= x^4  12x^3 + 62x^2  172x + 221
...