Let P x = x 2 + b x + c be a quadratic polynomial with real coefficients such that ∫ 0 1 P x d x = 1 and P x leaves remainder 5 when it is divided by x - 2 Then the value of 9 b + c is equal to:

Step-by-step solution

∫ 0 1 x 2 + b x + c d x = 1 1 3 + b 2 + c = 1    ⇒   b 2 + c = 2 3 3 b + 6 c = 4   . . . 1 P 2 = 5 4 + 2 b + c = 5 2 b + c = 1   . . . 2 From 1   &   2 b = 2 9   &   c = 5 9 9 b + c = 7