Given: -9i zero and
[tex]f(x)=x^4+11x^3+99x^2+891x+1458[/tex]
Find: root of the given eqaution.
Explanation: if -9i is thr one root of the equation then 9i wll be the another root of the equation.
-9i (x+9i)
9i (x-9i)
that means (x+9i)(x-9i) will be divide by the given equation.
[tex](x+9i)(x-9i)=(x^2+81)[/tex]
when we divide it to the given equation we get,
[tex]x^2+11x+18[/tex]
on solving it
[tex]\begin{gathered} x^4+11x^3+99x^2+891x+1458=(x+9i)(x-9i)(x^2+11x+18) \\ =(x+9i)(x-9i)(x+2)(x+9) \end{gathered}[/tex]
Hence,the other roots of the given eqaution is -2 and -9.
Final answer: the required roots of the equation is 9i,-9i,-2,-9.
