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Question

For what values of m will the equation x2bxaxc=m1m+1 have roots equal in magnitude but opposite sign?

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Solution

Given equation is x2bxaxc=m1m+1
It can also be written as (m+1)x2(b(m+1)+a(m1))x+c(m1)=0
Given that the equation have roots equal in magnitude but opposite in sign
Which means the sum of roots must be equal to zero
b(m+1)+a(m1)m+1=0
(a+b)m+ba=0
m=aba+b

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