Statement-1: If a, b, c are distinct real numbers, then `a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x` for each real x. Statement-2: `If a, b, c in R` such that `ax^(2) + bx + c = 0` for three distinct real values of x, then `a = b = c = 0` i.e. `ax^(2) + bx + c = 0` for all `x in R`.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.

Statement-1: If a, b, c are distinct real numbers, then `a((x-b)(x-c))

1.	Statement-1: If a, b, c are distinct real numbers, then `a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x` for each real x. Statement-2: `If a, b, c in R` such that `ax^(2) + bx + c = 0` for three distinct real values of x, then `a = b = c = 0` i.e. `ax^(2) + bx + c = 0` for all `x in R`.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.
Answer» Correct Answer - A Clearly, statement-2 is true (see Theory). Let `f(x) = a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x` Clearly, f(x) is a quadratic polynomial such that `f(a) = f(b) = f(c) = 0`. `therefore" "f(x) = 0 "for all" x in R" "["Using statement-2"]` So, statement-1 is true.

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