Answer:
5,[tex]i\sqrt 6[/tex] and [tex]-i\sqrt 6[/tex]
Step-by-step explanation:
We are given that the polynomial
[tex]f(x)=x^3-5x^2+6x-30[/tex]
We have to find the all the zeroes of the polynomial function.
[tex]f(x)=0[/tex]
[tex]x^3-5x^2+6x-30=0[/tex]
[tex]x^2(x-5)+6(x-5)=0[/tex]
[tex](x-5)(x^2+6)=0[/tex]
[tex]x-5=0[/tex]
[tex]x=5[/tex]
[tex]x^2+6=0[/tex]
[tex]x^2=-6[/tex]
[tex]x=\pm\sqrt{-6}=\pm i\sqrt6[/tex]
Using [tex]\sqrt{-1}=i[/tex]
Hence, all the zeroes of the polynomial function are
5,[tex]i\sqrt 6[/tex] and [tex]-i\sqrt 6[/tex]
