What can be inferred about the roots of a polynomial function if its graph touch

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Question: What can be inferred about the roots of a polynomial function if its graph touches the x-axis at a point?

Options:

Correct Answer: The root is a double root.

Solution:

If a polynomial function touches the x-axis at a point, it indicates that the root at that point is a double root.

What can be inferred about the roots of a polynomial function if its graph touches the x-axis at a point?

What can be inferred about the roots of a polynomial function if its graph touches the x-axis at a point?

Step 1: Understand what a polynomial function is. It is a mathematical expression that can be written in the form of ax^n + bx^(n-1) + ... + k, where a, b, and k are constants, and n is a non-negative integer.
Step 2: Know what the x-axis represents. The x-axis is the horizontal line on a graph where the value of y is zero.
Step 3: Recognize what it means for the graph to touch the x-axis. If the graph touches the x-axis at a point, it means that the function's value is zero at that point, indicating a root.
Step 4: Identify the type of root. If the graph touches the x-axis but does not cross it, this means that the root at that point has a multiplicity of at least 2, which is called a double root.
Step 5: Conclude that touching the x-axis means the root is a double root. Therefore, if a polynomial function touches the x-axis at a point, it indicates that the root at that point is a double root.

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