Question

question: 4
consider the following:
$f(x) = x^2 - 2x - 3$
where is the function $f(x)$ equal to zero?
a. $x = -1$ and $x = 3$
b. $x = 1$ and $x = 3$
c. $x = -1$ and $x = -3$
d. $x = 1$ and $x = -3$

Explanation:

Step1: Set the function to zero

To find where \( f(x) = 0 \), we set \( x^2 - 2x - 3 = 0 \).

Step2: Factor the quadratic equation

We factor the quadratic: \( x^2 - 2x - 3=(x - 3)(x + 1) \).

Step3: Solve for x

Set each factor equal to zero: \( x - 3 = 0 \) gives \( x = 3 \), and \( x + 1 = 0 \) gives \( x=-1 \).

Answer:

A. \( x = -1 \) and \( x = 3 \)