How to disprove a Fundamental Theory

Algebra Level 3

How many real roots does

(xa)(xb)(ca)(cb)+(xb)(xc)(ab)(ac)+(xa)(xc)(ba)(bc)=1\frac{(x-a)(x-b)}{(c-a)(c-b)}+\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-a)(x-c)}{(b-a)(b-c)}=1

have with abc0a\neq b\neq c\neq 0?

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