A) a+b+4=0
B) a+b-4=0
C) a-b-4=0
D) a-b+4=0
Correct Answer: A
Solution :
[a] Let\[\alpha ,\beta \]and \[\gamma ,\delta \]be the roots of the equations \[{{x}^{2}}+ax+b=0\]and \[{{x}^{2}}+bx+a=0\], respectively therefore, \[\alpha +\beta =-a,\alpha \beta =b\] And \[\delta +\gamma =-b,\gamma \delta =a.\] Given \[\left| \alpha -\beta \right|=\left| \gamma -\delta \right|\] \[\Rightarrow {{(\alpha +\beta )}^{2}}-4\alpha \beta ={{(\gamma +\delta )}^{2}}-4\gamma \delta \] \[\Rightarrow {{a}^{2}}-4b={{b}^{2}}-4a\] \[\Rightarrow ({{a}^{2}}-{{b}^{2}})+4(a-b)=0\] \[\Rightarrow a+b+4=0\] \[(\because a\ne b)\]
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