Urgent Maths problem help me!!?

Question

solve (a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d... ... show that a,b,c & d are in GP

Answer 1

discriminant=2sqrt[(ab+bc+cd)^2-(a^2+b^2...

= 2sqrt[2a(b^2)c+2b(c^2)d+2abcd-(ac)^2-(ad...

on applying GP properties

= 2 sqrt[2(ac)^2+2(bd)^2+2abcd-(ac)^2-(ad)^2...

=2 sqrt[2abcd-(ad)^2-(bc)^2]

= 2i sqrt[ad+bc]^2

=2i [ad+bc]

=2i [2bc] [again by GP property]

=4ibc

Hence the roots are p=[(ab+bc+cd)+2ibc]/(a^2+b^2+c^2)

and

[(ab+bc+cd)-2ibc]/(a^2+b^2+c^2)

Answer 2

the condition for a,b,c,d to be in GP is

ac = bd  

please simplify u r equation

i can't get u r full equation , its just  ............ in front of show that?

Answer 3

(a^2+b^2+c^2)p^2 - 2(ab+bc+cd)p + (b^2+c^2+d^2) = 0

Show that a,b,c & d are in Geometric Progression.

Impossible to prove with the given data. It is possible that a=b=c=d=0.