For the equation x + a 1 − x + b 1 = x + c 1 , if the product of roots is zero, then the sum of roots is

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2009

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For the equation $\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$ , if the product of roots is zero, then the sum of roots is

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$\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$ or $x^{2} + (a + b) x + ab = (b - a) x + (b - a) c$ or $x^{2} + 2 ax + ab + ca - bc = 0$ Since product of the roots $= 0$ $ab + c a - b c = 0; a = \frac{b c}{b + c}$ Thus sum of roots $= - 2 a = \frac{- 2 b c}{b + c}$

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2009

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