Question

Find a polynomial function of the lowest degree, with real coefficients, with the given roots.
Roots: -4, i, 5
A) f(x) = x4 - x3 - 19x2 - x - 20
B) f(x) = x4 + x3 - 19x2 + x - 20
C) f(x) = x3 - (1 + i)x2 - (20 - i)x + 20i
D) f(x) = x3 + (1 + i)x2 - (20 + i)x + 20i

Answer 1

Answer:

D

Step-by-step explanation:

Roots into factors:

x = -4 ----> (x + 4)

x = i -----> (x - i)

x = 5 -----> (x - 5)

(x + i)(x - 4)(x + 5)

(x - i)(x² - 4x + 5x - 20)

(x - i)(x² + x - 20)

x³ + x² - 20x - (ix² + ix - 20i)

x³ + (1 - i)x² - (20 + i)x + 20i