If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the product of the roots is (-1/2) (a² + b²).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 14E
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If the sum of the roots of the equation 1/(x + a) + 1/(x + b)
= 1/c is zero, then prove that the product of the roots is (-1/2)
(a² + b²).
Transcribed Image Text:If the sum of the roots of the equation 1/(x + a) + 1/(x + b) = 1/c is zero, then prove that the product of the roots is (-1/2) (a² + b²).
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