expend the determinats

a[-(2bα+3c)² ]-b[-(2bα+3c)(2aα+3b)]+ (2aα+3b)[b(2bα+3c)-c(2aα+3b)]=0

-a(2bα+3c)² + b(2bα+3c)(2aα+3b)+(2aα+3b)[2b^2 α+3bc-3bc-2acα]=0

(2bα+3c) [-2abα-3ac+2abα+3b² ]+ (2aα+3b)(2α)( b² -ac)=0

(2bα+3c) [-3ac +3b² ]+ (2aα+3b)(2α)( b²-ac)=0

(b² – ac)[4aα² + 12bα + ac] = 0=

CASE1→(b² -ac)=0

b² =ac {abc are in Gp}

CASE2→(4aα² +12bα+ac)=0 {Whose one root is }