How to disprove a Fundamental Theory

Algebra Level 3

How many real roots does

\(\frac{(x-a)(x-b)}{(c-a)(c-b)}+\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-a)(x-c)}{(b-a)(b-c)}=1\)

have with \(a\neq b\neq c\neq 0\)?

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