Use the given zero to find the remaining zeros of the functi

Use the given zero to find the remaining zeros of the function. f(x) = x^3 - 4x^2 + 16x - 64; zero: -4i Enter the remaining zeros of f. (Use a comma to separate answers as needed.)

Solution

x=4i 1 -4 16 -64

0 -4i 16i-16 64

1 -4-4i 16i 0

x^2 - (4+4i)x + 16i = 0

x = ((4+4i) +- sqrt(16-16+32i-64i)) / 2

= (4+4i +- sqrt(-32i)) / 2

= ( 4+4i +- ( 4sqrt(2i) )i ) / 2

x = 2+2i + ( 2sqrt(2i) )i

or

x = 2+2i - ( 2sqrt(2i) )i