Question

The equation $\frac{a(x-b)(x-c)}{(a-b)(a-c)}+\frac{b(x-c)(x-a)}{(b-c)(b-a)}+\frac{c(x-a)(x-b)}{(c-a)(c-b)}=x$ is satisfied $by$ :

• A. no value of $x$
• B. exactly two values of $x$
• C. exactly three values of $x$
• D. all values of $x$.

Answer 1

Answer: (D)

Note that $x=a$ or $b$ or $c$ satisfy more than two roots $\Rightarrow$ identity