Respuesta :
The zeros of the polynomial function: f(x) = x^3 – 5x^2 -6x is -1, 0, 6.
Solution:
Given, polynomial equation is [tex]x^{3}-5 x^{2}-6 x[/tex]
We have to find the zeroes of the given polynomial.
So, let us equate it with 0.
[tex]\begin{array}{l}{\text { Then, } x^{3}-5 x^{2}-6 x=0} \\\\ {\rightarrow x\left(x^{2}-5 x-6\right)=0} \\\\ {\rightarrow x\left(x^{2}-(6-1) x-6\right)=0} \\\\ {\rightarrow x\left(x^{2}-6 x+x-6\right)=0} \\\\ {\rightarrow x(x(x-6)+1(x-6))=0} \\\\ {\rightarrow x(x-6)(x+1)=0} \\\\ {\rightarrow x=0 \text { or } x-6=0 \text { or } x+1=0} \\\\ {\rightarrow x=0 \text { or } 6 \text { or }-1}\end{array}[/tex]
Hence, the roots of the given polynomial are -1, 0, 6.
