The expression ax² + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?

1, 3, 1

1, 2, 1

2, 1, 1

1, 1, 3

Correct answer is D

At x = 1, substituting x = 1 in the equation: ax² + bx + c = 5;
f(1) => a + b + c = 5 .....(1)

Taking the first derivative of f(x) in the original equation gives dy/dx = 2ax + b = 2x + 1 (given)....(2)

From (2),=> b = 1, and 2ax = 2x, => a = 1.

substituting into (1) 1 + 1 + c = 5, => c = 5 - 2 = 3

Thus a = 1, b = 1 and c = 3

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