Option C
The zeros of the polynomial function f(x) = x^3 - 5x^2 - 6x is x = 0 and x = -1 and x = 6
Solution:
Given that polynomial function is f(x) = x^3 - 5x^2 - 6x
We have to find the zeros of polynomial
To find zeros, equate the given polynomial function to 0. i.e f(x) = 0
[tex]x^3 - 5x^2 - 6x = 0[/tex]
Taking "x" as common term,
[tex]x(x^2 - 5x - 6) = 0[/tex]
Equating each term to zero, we get
[tex]x=0 \text { and } x^{2}-5 x-6=0[/tex]
Thus one of the zeros of function is x = 0
Now let us solve [tex]x^{2}-5 x-6=0[/tex]
We can rewrite -5x as -6x + x
[tex]x^2 + x - 6x - 6 = 0[/tex]
Taking "x" as common from first two terms and -6 as common from next two terms
[tex]x(x + 1) -6(x + 1) = 0[/tex]
Taking (x + 1) as common term,
(x + 1)(x - 6) = 0
x + 1 = 0 and x - 6 = 0
x = -1 and x = 6
Thus the zeros of given function is x = 0 and x = -1 and x = 6
