An algebra problem by Aditya Keshri
Algebra
Level
pending
If a,b,p,q are non-zero real numbers,then two equations 2a^{2}x^{2} - 2abx + b^{2}=0 and p^{2}x^{2} + 2pqx + q^{2} =0 have:
one common root if 2a^{2} + b^{2}=p^{2}+q^{2}
no common root
two common roots if 3pq=2ab
two common roots if 3qb=2ap
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