Question

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

Answer 1

False

Answer 2

The given equation is a Lagrange interpolating polynomial. If $a, b, c$ are distinct, the left-hand side is identically equal to 1 for all $x$. Thus, the equation becomes $1=1$, which is true for all $x$, meaning it has infinitely many roots. Therefore, it does not have exactly two roots.