noboa7
Answered

What are the excluded values of [tex]x[/tex] for [tex]\frac{x+4}{-3x^2 + 12x + 36}[/tex]?

A. [tex]x = -6, x = 2[/tex]
B. [tex]x = -6, x = -3, x = 2[/tex]
C. [tex]x = -2, x = 6[/tex]
D. [tex]x = -2, x = 3, x = 6[/tex]



Answer :

GinnyAnswer
To determine the excluded values of [tex]\( x \)[/tex] for the function [tex]\(\frac{x+4}{-3x^2 + 12x + 36}\)[/tex], we need to find the values of [tex]\( x \)[/tex] that make the denominator equal to zero. Excluded values occur at these points because division by zero is undefined in mathematics.

Let's follow these steps to find the excluded values:

1. Identify the Denominator:
[tex]\[ -3x^2 + 12x + 36 \][/tex]

2. Set the Denominator Equal to Zero:
[tex]\[ -3x^2 + 12x + 36 = 0 \][/tex]

3. Solve for [tex]\( x \)[/tex]:
We need to solve the quadratic equation [tex]\(-3x^2 + 12x + 36 = 0\)[/tex].

The solutions to this quadratic equation are:
[tex]\[ x = -2 \quad \text{and} \quad x = 6. \][/tex]

These values make the denominator zero, thereby causing the fraction to be undefined. Thus, the excluded values of [tex]\( x \)[/tex] are:

[tex]\[ x = -2 \quad \text{and} \quad x = 6. \][/tex]

So, the correct choice from the given options is:

[tex]\[ \boxed{x = -2, x = 6} \][/tex]