If a,b,c are the roots of the equation x3−3x2+3x+7=0, then the value of |2bc−a2c2b2c22ac−b2a2b2a22ab−c2| is

|abcbcacab||−a−b−ccabbca|=|abcbcacab|2 (3abc−a3−b3−c3)2=0

If a,b,c are the roots of the equation x3−3x2+3x+7=0, then the value of |2bc−a2c2b2c22ac−b2a2b2a22ab−c2| is

|abcbcacab||−a−b−ccabbca|=|abcbcacab|2 (3abc−a3−b3−c3)2=0

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If a,b,c are the roots of the equation $x^{3} - 3 x^{2} + 3 x + 7 = 0,$ then the value of $| \begin{matrix} 2 b c - a^{2} & c^{2} & b^{2} \\ c^{2} & 2 a c - b^{2} & a^{2} \\ b^{2} & a^{2} & 2 a b - c^{2} \end{matrix} |$ is

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Detailed Solution

$| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} | | \begin{matrix} - a & - b & - c \\ c & a & b \\ b & c & a \end{matrix} | = {| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} |}^{2} {(3 a b c - a^{3} - b^{3} - c^{3})}^{2} = 0$