If $3x^{2}-2(a-d)x+(a^{2}+2(b^{2}+c^{2})+d^{2})=2(ab+bc+cd)$, then If $3x^{2}-2(a-d)x+(a^{2}+2(b^{2}+c^{2})+d^{2})=2(ab+bc+cd)$, then

$A.$ a,b,c,d are in G.P.
$B.$ a,b,c,d are in H.P.
$C.$ a,b,c,d are in A.P.
$D.$ None of the above

Tried writing the expression as a sum of squares but it was of no use.

NOTE: G.P.- Geometric progression, H.P.-Harmonic Progression and A.P.-Arithmetic Progression. $x,a,b,c,d \in \mathbb{R}$
I wrote and put it in the jpg format.



I hope it helps!
I wrote and put it in the jpg format.



I hope it helps!