Let P(x) be a quadratic polynomial with real coefficients such that for all real x the relation `2(1 + P (x)) = P(x-1) + P(x + 1)` holds. If `P(0)=8` and `P(2) = 32`, then Sum of all the coefficients of `P(x)` is:

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let P(x) be quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then

Let P(x) be quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then (A) -12 (B) -15 (C) -17 (D) -5

Let p(x) be a quadratic polynomial with real coefficient such that for all real x, the relation 2(-1+ p(x)) = p(x-1) + p(x + 1) holds if p(0)=4, p(2)=16. 1) The sum of all coefficient of p(x) is 2) Coefficient of x is 3) If the range of p(x) is (-oo, m), then the value of m is

Let Q(x) be a quadratic polynomial with real coefficients such that for all real x the relation, 2(1+Q(x)) =Q(x - 1) +Q(x +1) holds good. If Q(0) = 8 and Q(2) = 32 then The number of integral values of 'x' for which Q(x) gives negative real values.

Let Q(x) be a quadratic polynomial with real coefficients such that for all real x the relation, 2(1+Q( x)) =Q(x - 1) +Q(x +1) holds good. If Q(0) = 8 and Q(2)= 32 then The range of Q(x) contains 'n' distinct negative integral values then the sum of these values is

Let P(x) be a polynomial of degree n with real coefficients and is non negative for all real x then P(x) + P^(1)(x)+ ...+P^(n)(x) is