Question

Which polynomial equations have -i as one of their roots? A) x3 + 5x2 - 20 = 0

B) x3 - x2 + x - 1 = 0
C) x3 + 3x2 + x + 3 = 0
D) x3 - 2x2 + x - 2 = 0
E) x3 - 6x2 - 16x + 96 = 0

Answer 1

the 2nd, 3rd, and 4th ones

Answer 2

Equation B, C and D have -i as one of their roots

Explanation:

We have to check the polynomial equations that have -i as one of the roots.

Thus, we have to check whether

`f(-i) = 0`

A)

`f(x) x^3 + 5x^2 - 20 = 0\\f(-i) = (-i)^3 + 5(-i)^2 - 20 \\eq 0`

B)

`f(x) x^3 -x^2 + x - 1 = 0\\f(-i) = (-i)^3 - (-i)^2 -i -1 = i + 1-i-1= 0`

C)

`f(x) x^3 +3x^2 + x + 3 = 0\\f(-i) = (-i)^3 +3 (-i)^2 -i +3 = i -3-i+3= 0`

D)

`f(x) x^3 -2x^2 + x -2= 0\\f(-i) = (-i)^3 -2 (-i)^2 -i -2 = i +2-i-2= 0`

E)

`F(x) = x^3 - 6x^2 - 16x + 96 = 0 \\f(-i) = (-i)^3 -6(-i)^2+16i+96 \\eq 0`