`P(x)=x^2+bx+c , int_0^1 P(x)dx=1 ` where `P(x)` is divisible by (x-2) then rem. is 5,9 (b+c)= ?

Let P(x)=x^(2)+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:

P(x) is a least degree polynomial such that (P(x)-1) in divisible by (x-1)^(2) and (P(x)-3) is divisible by ((x+1)^2) ,then (A) graph of y=P(x) ,is symmetric about origin (B) y=P(x) ,has two points of extrema (C) int_(-1)^(2)P(x)dx=0 for exactly one value of lambda . (D) int_(-1)^(2)P(x)dx=0 for exactly two values of lambda

integral of p(x)/(ax^(2)+bx+c)dx where p(x) is of degree 2 or more

If "log"_(ax)x, "log"_(bx) x, "log"_(cx)x are in H.P., where a, b, c, x belong to (1, oo) , then a, b, c are in

int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C , where

If p(x) = x^3 - 3x^2 + 2x + 5 and p(a) = p(b) = p(c) = 0 , then the value of (2-a) (2-b) (2-c) is.