Question

Find the zeros of the function. Select all the answers that apply.

f(x) = -x^3 + x^2 + 25x - 25
A. -1
B. 1
C. 5
D. -5

Answer 1

first group the first 2 together and the 3rd and fourth together

(-x^3 + x^2)(+25x-25)

GET OUT THAT UGLY NEGATIVE

-1(x^3 - x^2) (+25x - 25)

then find the gcf and forget that ugly negative

x^2 (x - 1) 25 (x-1)

then do whatever this is called

(x^2 + 25) (x - 1)

then you gotta factor (x^2 + 25)

(x+5)(x+5)(x-1)

NOW EQUAL THEM TO 0

x+5 = 0
x = -5

x - 1 = 0
x = 1


BOOM YOUR ZEROS ARE 1 AND -5

Answer 2

To find the zeros of the function f(x) = -x^3 + x^2 + 25x - 25, we set the function equal to zero and solve for x. The zeros of the function are x = -25, x = 1, and x = 1.

Step-by-step explanation:

To find the zeros of the function f(x) = -x^3 + x^2 + 25x - 25, we set the function equal to zero and solve for x. So, -x^3 + x^2 + 25x - 25 = 0. We can factor out a -1 from the first two terms to get x^3 - x^2 - 25x + 25 = 0. From here, we can use synthetic division or long division to divide the polynomial by (x - 1). By doing so, we find that (x - 1) is a factor of the polynomial. We can use this factor to factor out the polynomial as (x - 1)(x^2 + 24x - 25) = 0. Setting each factor equal to zero, we find that x - 1 = 0 and x^2 + 24x - 25 = 0. Solving the first equation, we get x = 1. For the second equation, we can use the quadratic formula to find the zeros. So, x = (-24 ± sqrt(24^2 + 4(1)(25))) / 2(1). Simplifying this, we get x = (-24 ± sqrt(576 + 100)) / 2, which is x = (-24 ± sqrt(676)) / 2. Therefore, x = (-24 ± 26) / 2, which gives us x = -25 or x = 1. Combining the zeros we found, the zeros of the function f(x) = -x^3 + x^2 + 25x - 25 are x = -25, x = 1, and x = 1. Therefore, the correct answers are A. -1 and B. 1.