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Let P(x)=x^(2)+bx+c be a quadratic polyn...

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:

A

15

B

7

C

9

D

11

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Knowledge Check

  • Let P(x) be a polynomial with real coefficients such that int_(0)^(1)x^(m) P(1 -x)dx = 0 AA minNcup{0} , then

    A
    `P(x) =x^(n) (1-x)^(n)` for some `n in N`
    B
    P(x) = `(1-x)^(2n)` for some `n in N`
    C
    P(x) = `1 -x^(m) (1 -x)^(n)` for some m, `n in N`
    D
    P(x)=0

  • Given ax^(2)+bx+c is a quadratic polynomial in x and leaves remainders 6 , 11 and 18 , respectively, when divided by (x+1), (x+2)and(x+3) . Find the value of a + b + c.

    A
    1
    B
    2
    C
    3
    D
    4

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