Respuesta :
first factor out a variable: x(x^2-2x-24)
now solve the quadratic: x(x-6)(x+4)
When you set these expressions equal to zero, you get 0, 6, and -4 as your answers.
now solve the quadratic: x(x-6)(x+4)
When you set these expressions equal to zero, you get 0, 6, and -4 as your answers.
The zeroes of the polynomial function are 0, 6, and -4.
Given that,
Polynomial function; [tex]\rm f(x) = x^3-2x^2-24x[/tex].
We have to determine,
The zeroes of the polynomial,
According to the question,
To determine the zeroes of the given polynomial function following all the steps given below.
Polynomial function; [tex]\rm f(x) = x^3-2x^2-24x[/tex].
Factorize the polynomial function to find the zeroes of the function,
[tex]\rm x^3-2x^2-24x =0\\\\\rm x(x^2-2x-24)=0\\\\x(x^2-6x+4x-24)=0\\\\x(x(x-6)+4(x-6))=0\\\\x ( (x-6) (x+4)) =0\\\\x (x-6) (x+4) =0[/tex]
Therefore,
The zeroes of the polynomial function are,
[tex]\rm x = 0\\\\x - 6 =0, \ \ x =6\\\\x +4 =0, \ \ x = -4[/tex]
Hence, The zeroes of the polynomial function are 0, 6, and -4.
For more details refer to the link given below.
https://brainly.com/question/15849916
