Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that [_0^1 P(…

Question

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

Solutions · 1