f(x)is a monic cubic polynomial with real coefficients. f(x) has 7+4i as a root and f(0)=−2145 . What is the coefficient of x in f(x) ?

Answer 1

as you know, the complex roots come in conjugate pairs. So, the other root is 7-4i

f(x) = (x-(7+4i))(x-(7-4i))(x-k)
= (x^2-14x+65)(x-k)

f(0) = 65(-k) = -2145
so, k = 33

f(x) = (x^2-14x+65)(x-33)
= x^3 - 47x^2 + 6527x - 2145

Answer 2

you mean 527.
Thanks a lot

Answer 3

Dang. A typo in the only place it mattered!