roots of equ

[rupsk]

The condition that the roots of (x-a)/ (ax+1) = (x+b)/ (bx+1) are reciprocal to each other is


A. a - b = 0
B. b = 0
C. a = 0
D. a + b = 0
E. None of these

I picked B which is incorrect.

[Anurag@Gurome]

The condition that the roots of (x-a)/ (ax+1) = (x+b)/ (bx+1) are reciprocal to each other is...

The equation is a quadratic equation and it will have two roots. If the roots are reciprocal to each other then the product of the roots will be 1.

--> (x - a)/(ax + 1) = (x + b)/(bx + 1)
--> (x - a)(bx + 1) = (x + b)(ax + 1)
--> (bx² - abx + x - a) = (ax² + abx + x + b)
--> (a - b)x² + 2abx + (a + b) = 0

Hence, product of the roots = (a + b)/(a - b)

If the roots are reciprocal to each other, (a + b)/(a - b) = 1
--> (a + b) = (a - b)
--> b = 0

The correct answer is B.

[rupsk]

I did the same but i got wrong answer so thought of asking others if I had wrong approach or missed out in calculation. Once again thanks.