QJEEM21Ma84cd: JEE Main 2021 Mathematics - Class 12 JEEM21Ma84cd Solution: Let P(x) = x 2 + bx + c be a quadratic polynomial with real…

Question

Verified Solution • 2025–26 Session moderate

Let P(x) = x² + bx + c be a quadratic polynomial with real coefficients such that

\int_0^1 {P(x)dx}

= 1 and P(x) leaves remainder 5 when it is divided by (x

-

2). Then the value of 9(b + c) is equal to :

Accepted Answer

(x - 2)Q(x) + 5 = {x^2} + bx + c

Put x = 2

5 = 2b + c + 4 .... (1)

\int_0^1 {({x^2} + bx + c)dx} = 1

\Rightarrow {1 \over 3} + {b \over 2} + c = 1

{b \over 2} + c = {2 \over 3}

.... (2)

Solve (1) & (2)

b = {2 \over 9}

c = {5 \over 9}

9(b + c) = 7

Step-by-Step Verified Solution