Q. For the equation $\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$, if the product of the roots is zero, then the sum of the roots is
A) 0
B) $\frac{2ab}{b + c}$
C) $\frac{2bc}{b + c}$
D) $- \frac{2bc}{b + c}$
Explanation
(d)
Since, $\frac{b - a}{x^{2} + (a + b)x + ab} = \frac{1}{x + c}$
$\ \Rightarrow x^{2} + 2ax + ab + ca - bc = 0$
Since, the product of roots is zero
Then, $ab + ca - bc = 0\ \Rightarrow a = \frac{bc}{b + c}$
$\therefore$ Sum of roots$= - 2a = \frac{- 2bc}{b + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.