if a,b,c,d and p are distinct real numbers such that

$\displaystyle (a^2 +b^2 +c^2 )p^2 -2(ab + bc + cd)p+(b^2 + c^2 + d^2) $is less than or equal to zero..

then prove that$\displaystyle a,b,c,d$ are in geometric progression.

thanks for you reply.