Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

Mathieu is finding the [tex]$x$[/tex]-intercepts of the function [tex]$f(x)=x^2+4x+3$[/tex]. His work is shown below.

1. [tex]0=x^2+4x+3[/tex]
2. [tex]0=(x+3)(x+1)[/tex]
3. [tex]x+3=x+1[/tex]
4. [tex]x=x-2[/tex]
5. [tex]0=-2[/tex]
6. There are no [tex][tex]$x$[/tex][/tex]-intercepts.

Which error did Mathieu make?

A. He factored incorrectly.
B. He did not use the constant as the [tex]$x$[/tex]-intercept.
C. He set the factored expressions equal to each other.
D. He incorrectly solved the equation [tex]$x+3=x+1$[/tex].


Sagot :

To find the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = x^2 + 4x + 3 \)[/tex], we follow these steps:

1. Set the function equal to zero:
[tex]\[ 0 = x^2 + 4x + 3 \][/tex]

2. Factor the quadratic equation:
[tex]\[ 0 = (x + 3)(x + 1) \][/tex]

3. Set each factor equal to zero:
[tex]\[ x + 3 = 0 \quad \text{or} \quad x + 1 = 0 \][/tex]

4. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \][/tex]
[tex]\[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \][/tex]

Therefore, the [tex]\( x \)[/tex]-intercepts are [tex]\( x = -3 \)[/tex] and [tex]\( x = -1 \)[/tex].

Now, let's analyze Mathieu's steps:

1. [tex]\( 0 = x^2 + 4x + 3 \)[/tex]
2. [tex]\( 0 = (x + 3)(x + 1) \)[/tex]

So far, Mathieu's work is correct.

3. [tex]\( x + 3 = x + 1 \)[/tex]

This is where Mathieu made an error. Instead of setting each factor equal to zero, he set the factored expressions equal to each other.

4. [tex]\( x = x - 2 \)[/tex]
5. [tex]\( 0 = -2 \)[/tex]
6. Concluded that there are no [tex]\( x \)[/tex]-intercepts.

Because of his error in step 3, his subsequent steps and conclusion are incorrect.

Error Identified:
Mathieu made an error in step 3. He should have set each factor equal to zero rather than setting the factored expressions equal to each other.

The correct identification of the error:
He set the factored expressions equal to each other.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.