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 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 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)=x^(2)+(1)/(2)x+b and Q(x)=x^(2)+cx+d be two polynomials with real coefficients such that P(x)Q(x)=Q(P(x)) for all real x. Find all the real roots of P(Q(x))=0

If the coefficient of x^(2) in the exapansion of (x)/((2x+1)(x-2)) is (P)/(Q), then P+Q=

Let f(x)={(x^3+2x^2,x in Q),(-x^3+2x^2+ax, x !in Q)) , then the integral value of 'a' so that f(x) is differentiable at x=1 is

Let P(x)=x^3+ax^2+bx+c be a polynomial with real coefficients, c!=0andx_1,x_2,x_3 be the roots of P(x) . Determine the polynomial Q(x) whose roots are 1/x_1,1/x_2,1/x_3 .