Answer:
Equation B, C and D have -i as one of their roots
Step-by-step explanation:
We have to check the polynomial equations that have -i as one of the roots.
Thus, we have to check whether
[tex]f(-i) = 0[/tex]
A)
[tex]f(x) x^3 + 5x^2 - 20 = 0\\f(-i) = (-i)^3 + 5(-i)^2 - 20 \neq 0[/tex]
B)
[tex]f(x) x^3 -x^2 + x - 1 = 0\\f(-i) = (-i)^3 - (-i)^2 -i -1 = i + 1-i-1= 0[/tex]
C)
[tex]f(x) x^3 +3x^2 + x + 3 = 0\\f(-i) = (-i)^3 +3 (-i)^2 -i +3 = i -3-i+3= 0[/tex]
D)
[tex]f(x) x^3 -2x^2 + x -2= 0\\f(-i) = (-i)^3 -2 (-i)^2 -i -2 = i +2-i-2= 0[/tex]
E)
[tex]F(x) = x^3 - 6x^2 - 16x + 96 = 0 \\f(-i) = (-i)^3 -6(-i)^2+16i+96 \neq 0[/tex]
