For the function f(x) = x³ − 6x² + ax + b, it is given f(1) = f(3) = 0. The values of a and b are: A. a = 11, b = −6 B. a = −11, b = 6 C. a = 6, b = −11 D. a = −6, b = 11 Answer: A) a = 11, b = −6 Explanation: f(1) = 1 − 6 + a + b = 0 → a + b = 5. f(3) = 27 − 54 + 3a + b = 0 → 3a + b = 27. Solving: 2a = 22 → a = 11, b = −6.

imo class 12 continuity and differentiability

For the function f(x) = x³ − 6x² + ax + b, it is given f(1) = f(3) = 0. The values of a and b are:

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For the function f(x) = x³ − 6x² + ax + b, it is given f(1) = f(3) = 0. The values of a and b are:

Answer: A) a = 11, b = −6

Explanation: f(1) = 1 − 6 + a + b = 0 → a + b = 5. f(3) = 27 − 54 + 3a + b = 0 → 3a + b = 27. Solving: 2a = 22 → a = 11, b = −6.