Which of the following statements is true about the roots of a polynomial functi

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Question: Which of the following statements is true about the roots of a polynomial function?

Options:

Correct Answer: A polynomial can have at most as many roots as its degree.

Solution:

A polynomial function can have at most as many roots as its degree, but not all roots need to be real.

Which of the following statements is true about the roots of a polynomial function?

Which of the following statements is true about the roots of a polynomial function?

Step 1: Understand what a polynomial function is. A polynomial function is a mathematical expression that includes variables raised to whole number powers, like x^2 + 3x + 2.
Step 2: Identify the degree of the polynomial. The degree is the highest power of the variable in the polynomial. For example, in x^2 + 3x + 2, the degree is 2.
Step 3: Know that the number of roots (solutions) a polynomial can have is related to its degree. A polynomial of degree n can have at most n roots.
Step 4: Realize that not all roots need to be real numbers. Some roots can be complex (involving imaginary numbers). For example, the polynomial x^2 + 1 has no real roots, but it has two complex roots.
Step 5: Conclude that the statement is true: A polynomial function can have at most as many roots as its degree, but not all roots need to be real.

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