If a b c 0 then one of the solution of ........

Mathematics (NDA) Matrices and Determinants

If a + b + c = 0, then one of the solution of $\begin{vmatrix} a-x & c &b \\ c& b-x &a \\ b & a & c-x \end{vmatrix}=0$

x=a

$x=\sqrt{\frac{3(a^{2}+b^{2}+c^{2})}{2}}$

$x=\sqrt{\frac{2(a^{2}+b^{2}+c^{2})}{3}}$

x=0

Given a + b + c = 0,
$\begin{vmatrix} a-x & c &b \\ c& b-x &a \\ b & a & c-x \end{vmatrix}=0$

Going through option, x=0
Hence option 4 is correct

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