The correct option is D a=b=c
ax2−2bx+c=0, bx2−2cx+a=0 and cx2−2ax+b=0 all have positive roots only.
Product of roots >0
⇒ca>0, ab>0, bc>0
⇒a,b,c have same sign.
Also, Δ≥0
⇒b2≥ac, c2≥ab, a2≥bc ⋯(1)
⇒b2c2≥ac⋅ab=a2bc, c2a2≥b2ac, a2b2≥c2ab
⇒bc≥a2, ac≥b2, ab≥c2 ⋯(2)
From (1) and (2),
a2=bc, b2=ac, c2=ab
⇒a3=b3=c3=abc
⇒a=b=c