At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x axis?
2 answers:
The answer for the exercise is: -2
The explanation is shown below:
You have the following function given in the problem above: f(x)=(x-5)³(x+2)². As you can see, (x+2)² is a double root, therefore, it touches the x-axis but it does nos cross it. Therefore, the answer is -2.
When you plot the function, you obtain the graph attached.
The explanation is shown below:
You have the following function given in the problem above: f(x)=(x-5)³(x+2)². As you can see, (x+2)² is a double root, therefore, it touches the x-axis but it does nos cross it. Therefore, the answer is -2.
When you plot the function, you obtain the graph attached.
We have that
f(x) = (x – 5)³(x + 2)²
we know that
<span>the roots can touch or cross the x axis
</span>The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.
(x - 5)³ has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)² has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
therefore
the answer is
<span>the graph of f(x) touch the x axis for the root x=-2
</span>
see the attached figure
f(x) = (x – 5)³(x + 2)²
we know that
<span>the roots can touch or cross the x axis
</span>The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.
(x - 5)³ has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)² has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
therefore
the answer is
<span>the graph of f(x) touch the x axis for the root x=-2
</span>
see the attached figure
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