Which of the following is true about the roots of a cubic function?

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

Options:

Correct Answer: It can have at most three real roots.

Solution:

A cubic function can have at most three real roots, and it is guaranteed to have at least one real root due to the Intermediate Value Theorem.

Which of the following is true about the roots of a cubic function?

Which of the following is true about the roots of a cubic function?

Step 1: Understand what a cubic function is. A cubic function is a polynomial function of degree three, which can be written in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a is not zero.
Step 2: Know that the roots of a function are the values of x that make the function equal to zero (f(x) = 0).
Step 3: A cubic function can have up to three roots. This means it can cross the x-axis at most three times.
Step 4: The Intermediate Value Theorem states that if a continuous function changes signs over an interval, then there is at least one root in that interval. Since cubic functions are continuous, they will always have at least one real root.
Step 5: Therefore, a cubic function will always have at least one real root and can have up to three real roots.

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