Question

The function f(x) = x2 - 5x - 6, written

correctly in factored form, and its zeros are
A. f(x) = (x - 2)(x + 3) with zeros of
-2 and 3
B. f(x) = (x+3)(x - 2) with zeros of
-3 and 2
C. f(x) = (x - 6)(x + 1) with zeros of
-6 and 1
D. f(x) = (x + 1)(x – 6) with zeros of
-1 and 6

Answer 1

The function f(x) = x² - 5x - 6 can be factored as (x-2)(x+3) with zeros of -2 and 3.

Step-by-step explanation:

The given function is f(x) = x² - 5x - 6. To find its factored form and zeros, we need to factorize the quadratic equation.

The factored form is given by f(x) = (x-2)(x+3) with zeros of -2 and 3. Therefore, the correct option is A.

Answer 2

D

Step-by-step explanation:

Given

f(x) = x² - 5x - 6

To find the zeros let f(x) = 0, that is

x² - 5x - 6 = 0

Consider the factors of the constant term (- 6) which sum to give the coefficient 0f the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

(x + 1)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6