Respuesta :
Option E
The real zeros of function are (-2, 3, -3)
Solution:
Given function is: [tex]x^3 + 2x^2 -9x - 18[/tex]
To find the zeroes of the function, we just need to evaluate the values and check if the function/expression tends to 0.
Let [tex]f(x) = x^3 + 2x^2 -9x - 18[/tex]
On grouping the terms we get,
[tex]f(x) = (x^3 + 2x^2) - (9x +18)[/tex]
Taking [tex]x^2[/tex] as common term from first two terms and "9" as common term from last two terms,
[tex]f(x) = x^2(x + 2) - 9(x + 2)[/tex]
Taking (x + 2) as common term,
[tex]f(x) = (x^2 - 9)(x + 2)[/tex]
[tex]f(x) = (x^2 - 3^2)(x + 2)[/tex]
We know that,
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
Applying the above identity,
[tex]f(x) = (x + 3)(x - 3)(x + 2)[/tex]
We equate the function to 0 , to find the zeros of polynomial function
(x + 3)(x - 3)(x + 2) = 0
Therefore zeros are:
x + 3 = 0
x = -3
x - 3 = 0
x = 3
x + 2 = 0
x = -2
Thus zeros are (-2, 3, -3) Option E is correct
Answer:
The real zeros of function are (-2, 3, -3)
Step-by-step explanation:
It was E on my computer but always double check to match!
