Answer:
The roots of the given equation is x=4,3i,-3i
Step-by-step explanation:
The given cubic equation is
[tex]y=x^3-4x^2+9x-36[/tex]
To find the roots we have to equate the equation to zero
ie, [tex]x^3-4x^2+9x-36=0[/tex]
It can be done by using Synthetic division method
Therfore [tex](x-1) is not a factor or root
now put x=-1
Therfore [tex](x-1) is not a factor or root
similarly let x=2,-2,3,-3 all not equal to zero so the are not roots.
let x-4 is a factor of given equation
then it satifies the equation ie (x-4) is a root
And it may be written as
[tex](x-4)(x^2+9)
