Question

Explain how to find the zero(s) of an equation when a function is in a factored (intercept) form.

A. Set the equation equal to zero and solve for the variable.
B. Use the quadratic formula to find the zeros.
C. Add the constants in the equation to find the zeros.
D. Please provide an answer.

Answer 1

Final answer:

To find the zero(s) of an equation when a function is in factored form, use the factored equation to set each factor equal to zero and solve for the variable.

Step-by-step explanation:

When a function is presented in factored (intercept) form, it indicates the roots or zeros of the function. The method involves setting each factor in the equation to zero and solving for the variable to determine the zeros. For instance, if the equation is in the form

`�(�)=(�−�)(�−�)(�−�)...=0`

`f(x)=(x−a)(x−b)(x−c)...=0, where �a, �b, �`

c, etc., are the intercepts, then setting each factor equal to zero (

`�−�=0x−a=0, �−�=0x−b=0, �−�=0x−c=0, etc.) allows you to solve for �`

x individually, giving the respective zeros of the function. This approach aids in identifying all the values of

`�x for which the function equals zero.`

Utilizing this method simplifies the process of finding zeros without having to expand or factorize further. It directly leverages the intercepts provided in the factored form, making it an efficient way to identify the roots of the equation. This method is particularly useful for polynomial equations, allowing for a straightforward extraction of the zeros.