1. Tardigrade
  2. Question
  3. Mathematics
  4. If a, b, c are distinct real numbers, then the quadratic expression ((x-b)(x-c)/(a-b)(a-c))+((x-c)(x-a)/(b-c)(b-a))+((x-a)(x-b)/(c-a)(c-b)) is identically equal to

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Q. If $a, b, c$ are distinct real numbers, then the quadratic expression $\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+\frac{(x-a)(x-b)}{(c-a)(c-b)}$ is identically equal to

Complex Numbers and Quadratic Equations

Solution:

Use the fact that expression becomes equal to 1 for $x=a, b, c$.