Question

Using Rolle’s theorem, the equation \( a_0x^n + a_1x^{n-1} + \dots + a_n = 0 \) has at least one root between 0 and 1 if,

• A. \( a_0 = 0 \)
• B. \( a_1 = 0 \)
• C. \( a_2 = 0 \)
• D. \( a_n = 0 \)

Hint:

Rolle’s theorem applies to continuous and differentiable functions and guarantees a root between two points if the function takes equal values at the endpoints.

Answer 1

The Correct Option is A

Rolle’s theorem guarantees at least one root if the function is continuous and differentiable, and the endpoints have the same value.