Answer:
Explanation:
To find the solutions to the equation f(x) = x^2 - 3x - 18, we can use the zero product property. This property states that if ab = 0, then either a = 0, b = 0, or both a and b are equal to 0.
In order to use the zero product property, we first need to factor the quadratic equation f(x) = x^2 - 3x - 18. We can do this by finding two numbers that multiply to -18 and add to -3. These numbers are -6 and 3, so we can write:
f(x) = x^2 - 3x - 18 = (x - 6)(x + 3)
Now we can use the zero product property to find the solutions to this equation. Setting each factor equal to 0 and solving for x gives:
x - 6 = 0 or x + 3 = 0
Solving these equations for x, we get:
x = 6 or x = -3
Therefore, the solutions to the equation f(x) = x^2 - 3x - 18 are x = 6 and x = -3.
To summarize, we used the zero product property to find the solutions to the quadratic equation f(x) = x^2 - 3x - 18 by first factoring it as (x - 6)(x + 3), setting each factor equal to 0, and solving for x.