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Question

Difference between the corresponding roots of x2+ax+b=0 and x2+bx+a=0 is same and a b, then
  1. a + b - 4 = 0
  2. a + b + 4 = 0
  3. a - b + 4 = 0
  4. a - b - 4 = 0


Solution

The correct option is B a + b + 4 = 0
Let α,β and γ,δ be the roots of the equations x2+ax+b=0 and x2+bx+a=0, respectively
α+β=a,αβ=b and γ+δ=b,γδ=a.Given|αβ|=|γδ|(αβ)2=(γδ)2(α+β)24αβ=(γ+δ)24γδa24b=b24a(a2b2)+4(ab)=0a+b+4=0(ab)

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