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Each question in this section has four choices (a), (b), (c) and (d) out of which only one is correct. Mark your choices as follows:
(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
Suppose \( a, b, c \) are distinct real numbers.
Let \( f(x)=\left|\begin{array}{lll}x^{3}+a^{3} & x^{2}-a^{2} & x+a \\ x^{3}+b^{3} & x^{2}-b^{2} & x+b \\ x^{3}+c^{3} & x^{2}-c^{2} & x+c\end{array}\right| \)
Statement-1: \( f(x) \) is a polynomial of degree 3 .
Statement-2: \( a, b, c \) are zeros of \( f(x) \).
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