Let `a ,b in na n a > 1.` Also `p` is a prime number. If `a x^2+b x+c=p` for any intergral values of `x ,` then prove that `a+b x+c!=2p` for any integral value of `xdot`

Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :

If X ~ B (6,p) and 2. P (X =3) =P (X= 2) then find the value of p

Let a,b, c be unequal real numbers.If a,b,c are in G.P.and a+b+c=bx, then 'x' can not lie in

If a,b,c are in G.P and a+x,b+x,c+x are in H.P,then the value of x is (a,b,c are distinct numbers)

If a, b, c are in A.P. and a, x, b, y, c are in G.P., then prove that b^(2) is the arithmatic mean of x^(2)" and "y^(2).

Let p = 144 ^(sin^(2)x) + 144^( cos^(2)x), then the number of integral values of such p's can take are

If a, b, c are in A.P. and x, y, z are in G.P., then prove that : x^(b-c).y^(c-a).z^(a-b)=1

Let P(x)=ax^(2)+bx+8 is a quadratic polynomial. If the minimum value of P(x) is 6 when x=2 , find the values of a and b.

Let P(a, b, c) be any on the plane 3x+2y+z=7 , then find the least value of 2(a^2+b^2+c^2) .