The Bisection Method requires the function to change sign over the interval [a, b]. What condition must be satisfied?  
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f(a) + f(b) = 0

f(a) × f(b) < 0

f(a) × f(b) > 0

f(a) = f(b)

The condition that must be satisfied for the Bisection Method is:

**\( f(a) \times f(b) < 0 \)**

This ensures that the function \( f(x) \) changes sign over the interval \([a, b]\), which is necessary for the method to work correctly in finding a root within that interval.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the Bisection Method used for?
2. How do you determine the midpoint in the Bisection Method?
3. Why is it important that \( f(a) \times f(b) < 0 \) in the Bisection Method?
4. What happens if \( f(a) \times f(b) > 0 \) in the Bisection Method?
5. How do you decide when to stop the Bisection Method?

**Tip:** Always check the signs of \( f(a) \) and \( f(b) \) before applying the Bisection Method to ensure a root exists in the interval.

Explore the condition required for the Bisection Method in numerical analysis: f(a) × f(b) < 0. Learn why this condition is crucial for ensuring the function changes sign over the interval [a, b], essential for accurate root finding in numerical methods.

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