Let `a ,b in N and 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 `ax^2+b x+c!=2p` for any integral value of `xdot`

p=3n(5n-2) q=4(2-5n) If p-q= ax^(2)=bx+c for all values of x where a,b and c are constants, what is the value of c?

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 :

a ,b ,c are positive real numbers forming a G.P. If ax^2+2b x+c=0 and dx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x 3

a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If a, b, c are in G.P. and also a, b, c are in A.P. Prove that: 1/a+1/c=2/b

If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db ,c respectively, then prove that a/x+c/y=2a n d1/x+1/y=2/b

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x >3.

If p = (x^(a+ b))/(x^b) , what is the value of positive integer p? (1) x = 5 (2) a = 0

If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P.