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If $f (x) = |\begin{array}{ccc} x - 3 & 2 x^{2} - 18 & 3 x^{3} - 81 \\ x - 5 & 2 x^{2} - 50 & 4 x^{3} - 500 \\ 1 & 2 & 3 \end{array}|$ ,then $f (1) \cdot f (3) + f (3) \cdot f (5) \cdot f (5) \cdot f (1)$ is equal to

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detailed solution

Correct option is B

f(1)=−2−16−78−4−48−496123f(3)=000−2−32−392123=0f(1)f(3)+f(3)f(5)f(5)f(1)=f(1)f(3)1+{f(5)}2=0×1+{f(5)}2=0

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If f(x)=x−32x2−183x3−81x−52x2−504x3−500123 ,then f(1)⋅f(3)+f(3)⋅f(5)⋅f(5)⋅f(1) is equal to

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If $f (x) = |\begin{array}{ccc} x - 3 & 2 x^{2} - 18 & 3 x^{3} - 81 \\ x - 5 & 2 x^{2} - 50 & 4 x^{3} - 500 \\ 1 & 2 & 3 \end{array}|$ ,then $f (1) \cdot f (3) + f (3) \cdot f (5) \cdot f (5) \cdot f (1)$ is equal to