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The sum of roots of equation 1/(x+a)+1/(...

The sum of roots of equation `1/(x+a)+1/(x+b)=1/c` is zero find the product of roots of equation a)0 b) `((a+b)/2)` c)`-((a^2+b^2)/2)` d) `2(a^2+b^2)`

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Given equation is ,
`1/(x+a)+1/(x+b) = 1/c`
`=>(x+b+x+a)c = (x+a)(x+b)`
`=>(2x+a+b)c = (x+a)(x+b)`
`=>(2x+a+b)c = = x^2+(a+b)x+ab`
`=>x^2+(a+b-2c)x+ab-(a+b)c = 0`
Sum of roots, `=-(a+b-2c)`
`a+b-2c = 0`, as sum of roots is given 0.
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