The number of real roots of the equation $$A^2/x + B^2/(x-1) = 1$$ , where A and B are real numbers not equal to zero simultaneously, is ?->(Show Answer!)

1. The number of real roots of the equation $$A^2/x + B^2/(x-1) = 1$$ , where A and B are real numbers not equal to zero simultaneously, is

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By: anil on 05 May 2019 02.30 am

The given equation can be written as : $$A^2 * (x-1) + B^2 * x = x^2 - x$$
=> $$x^2 + x(-1 - A^2 - B^2) + A^2 = 0$$
Discriminant of the equation = $$ (-1 - A^2 - B^2) ^2 - 4A^2$$
=$$ A^4 + B^4 + 1 - 2A^2 + 2B^2 + 2A^2B^2$$
= $$ A^4 + B^4 + 1 - 2A^2 - 2B^2 + 2A^2B^2 + 4B^2$$
= $$ (A^2 + B^2 - 1)^2 + 4B^2$$
>= 0, 0 when B =0 and A =1
Hence, the number of roots can be 1 or 2.
Option d) is the correct answer.

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MCQ-> I want to stress this personal helplessness we are all stricken with in the face of a system that has passed beyond our knowledge and control. To bring it nearer home, I propose that we switch off from the big things like empires and their wars to more familiar little things. Take pins for example! I do not know why it is that I so seldom use a pin when my wife cannot get on without boxes of them at hand; but it is so; and I will therefore take pins as being for some reason specially important to women.There was a time when pinmakers would buy the material; shape it; make the head and the point; ornament it; and take it to the market, and sell it and the making required skill in several operations. They not only knew how the thing was done from beginning to end, but could do it all by themselves. But they could not afford to sell you a paper of pins for the farthing. 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MCQ->The number of real roots of the equation $$A^2/x + B^2/(x-1) = 1$$ , where A and B are real numbers not equal to zero simultaneously, is....