Mathematics 2000 JAMB Past Questions - Question 40: 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?

Correct Answer

D

Explanation

To find the values of a, b, and c, we can use the given information that the expression ax² + bx + c equals 5 at x = 1.Substituting x = 1 into the expression, we have:a(1)² + b(1) + c = 5a + b + c = 5 ----(1)We are also given that the derivative of the expression is 2x + 1. The derivative of ax² + bx + c with respect to x is 2ax + b. Comparing this with 2x + 1, we can equate the corresponding coefficients:2a = 2 ----(2)b = 1 ----(3)From equation (2), we can solve for a:2a = 2a = 1Substituting the value of a into equation (3), we have:b = 1Now, we can substitute the values of a and b into equation (1) to find c:1 + 1 + c = 5c = 5 - 2c = 3Therefore, the values of a, b, and c are 1, 1, and 3, respectively.