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Question

If α is common root of both these equations
ax2+bx+c=0
bx2+cx+a=0,then
α2abc2=αcba2=1acb2

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Solution

Let α be the common root of the given equations ax2+bx+c=0 and bx2+cx+a=0
Then aα2+bα+c=0 and bα2+cα+a=0
Eliminating α as shown below(in the diagram part )we get
α2bac2=αcba2=1acb2

1060576_1183559_ans_a7a785e62518450abae3a282f15889ba.PNG

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