Answer:
Explanation:
complex roots always occur in pairs.
so two roots are 4-i and 4+i
[x-(4-i)] and [x-(4+i)] are factors of f(x)
or [(x-4)+i] and [(x-4)-i] are factors of f(x)
[(x-4)+i][(x-4)-i]=(x-4)²-i²=x²-8x+16-(-1)=x²-8x+17
x²-8x+17) x³ -5 x² -7 x +51( x+3
x³ -8x² +17x
- + -
________________
3x² -24x +51
3x² -24x +51
- + -
______________
0
______________
so one more factor is x+3
or zero =-3
Hence zeros of f(x) are -3,4-i,4+i