Answer:
The zeros of the given function are -9,-1 and 12.
Step-by-step explanation:
The given function is
[tex]f(x)=x^3-2x^2-111x-108[/tex]
It is given that the x-intercept of the graph is -9, therefore -9 is a zero of the function.
Since -9 is the zero of the function, therefore (x+9) is a factor of f(x). Use synthetics method or long division method to divide the function by (x+9).
[tex]f(x)=(x+9)(x^2-11x-12)=0[/tex]
[tex]f(x)=(x+9)(x^2-12x+x-12)=0[/tex]
[tex]f(x)=(x+9)(x(x-12)+(x-12))=0[/tex]
[tex]f(x)=(x+9)(x-12)(x+1)=0[/tex]
Use zero product property and quote each factor equal to 0.
[tex]x=-9,-1,12[/tex]
Therefore zeros of the given function are -9,-1 and 12.
