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What are the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = 4(x-5)(x-6) \)[/tex]?

Enter your answers in coordinate notation.

First [tex]\( x \)[/tex]-intercept: [tex]\(\square\)[/tex]
Second [tex]\( x \)[/tex]-intercept: [tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
To determine the [tex]$x$[/tex]-intercepts of the function [tex]\( f(x) = 4(x - 5)(x - 6) \)[/tex], we need to find the values of [tex]\( x \)[/tex] where [tex]\( f(x) = 0 \)[/tex].

The equation can be set to zero as follows:
[tex]\[ 4(x - 5)(x - 6) = 0 \][/tex]

For the product to be zero, at least one of the factors must be zero. Thus, we solve for [tex]\( x \)[/tex] as follows:
1. [tex]\( x - 5 = 0 \)[/tex]
2. [tex]\( x - 6 = 0 \)[/tex]

Solving these individually:
1. [tex]\( x - 5 = 0 \)[/tex]
[tex]\[ x = 5 \][/tex]
2. [tex]\( x - 6 = 0 \)[/tex]
[tex]\[ x = 6 \][/tex]

Therefore, the [tex]\( x \)[/tex]-intercepts are [tex]\( (5, 0) \)[/tex] and [tex]\( (6, 0) \)[/tex].

In coordinate notation, the [tex]$x$[/tex]-intercepts are:
First [tex]$x$[/tex]-intercept: [tex]\((5, 0)\)[/tex]
Second [tex]$x$[/tex]-intercept: [tex]\((6, 0)\)[/tex]
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