Urgent!!!!! If p,q,r are not in G P an d if detminant of given matrix is zero [ 1 q/p - Maths - Determinants

Question

Urgent!!!!!
If p,q,r are not in G P an d if detminant of given matrix is
zero [ 1 q/p α+q/p 1 r/q α +r/q pα+q qα+r
0]then prove that pα^2+2pα+r=0

Ajanta Trivedi · Accepted Answer

the given determinant is 11pa+qq/pr/qqa+ra+(q/p)a+(r/q)0=0
applying R1→R1-R201pa+q(q/p)-(r/q)(r/q)qa+r(q/p)-(r/q)a+(r/q)0=0taking qp-rq  common from 1st row:(qp-rq)01pa+q1(r/q)qa+r1a+(r/q)0=0
if qp-rq=0⇒q2-pr=0 i e  q2=pr but it is given that
p,q and r are not in GP
therefore
01pa+q1(r/q)qa+r1a+(r/q)0=0applying C2→C2-C301pa+q0-aqa+r1a+(r/q)0=0now expanding the determinant, we have1
[qa+r+a(pa+q)]=0qa+r+pa2+aq=0pa2+2aq+r=0

hope this helps you

Urgent!!!!! If p,q,r are not in G.P an d if detminant of given matrix is zero [ 1 q/p α+q/p 1 r/q α +r/q pα+q qα+r 0]then prove that pα^2+2pα+r=0

Urgent!!!!!

If p,q,r are not in G.P an d if detminant of given matrix is zero [ 1 q/p α+q/p 1 r/q α +r/q pα+q qα+r 0]then prove that pα^2+2pα+r=0