Question

If a,b,c,d are real then the roots of the given equation are?

Answer 1

1. All real roots

Explanation:

We can eliminate incorrect options by choosing `a, b, c, d` appropriately...

Let `a=b=1` and `c=d=-1`

Then:

`0 = 1/(x-a)+1/(x-b)+1/(x-c)+1/(x-d)`

`color(white)(0) = 2/(x-1)+2/(x+1)`

`color(white)(0) = (2((x+1)+(x-1)))/((x-1)(x+1))`

`color(white)(0) = (4x)/((x-1)(x+1))`

So `x = 0` is the only solution.

This allows us to eliminate options 2, 3 and 4, leaving option 1.