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 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 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 P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1,3) and Q(x)<0AA x in(-oo ,1)uu(3, oo) If sum of the roots of the equation P(x) =0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

Let P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1, 3) and Q (x)<0AA x in(-oo, 1)uu(3, oo) . If sum of the roots of the equation P(x)=0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

If p and q are ositive,then prove that the coefficients of x^(p) and x^(q) in the expansion of (1+x)^(p+q) will be equal.

If x=(p+q)/(p-q) and y=(p-q)/(p+q) then the value of (x-y)/(x+y) is