Define a polynomial $f ( x )$ by $$f ( x ) = \left| \begin{array} { l l l }
1 & x & x \\
x & 1 & x \\
x & x & 1
\end{array} \right|$$ for all $x \in \mathbb { R }$, where the right hand side above is a determinant. Then the roots of $f ( x )$ are of the form (A) $\alpha , \beta \pm i \gamma$ where $\alpha , \beta , \gamma \in \mathbb { R } , \gamma \neq 0$ and $i$ is a square root of $- 1$. (B) $\alpha , \alpha , \beta$ where $\alpha , \beta \in \mathbb { R }$ are distinct. (C) $\alpha , \beta , \gamma$ where $\alpha , \beta , \gamma \in \mathbb { R }$ are all distinct. (D) $\alpha , \alpha , \alpha$ for some $\alpha \in \mathbb { R }$.
Define a polynomial $f ( x )$ by
$$f ( x ) = \left| \begin{array} { l l l }
1 & x & x \\
x & 1 & x \\
x & x & 1
\end{array} \right|$$
for all $x \in \mathbb { R }$, where the right hand side above is a determinant. Then the roots of $f ( x )$ are of the form\\
(A) $\alpha , \beta \pm i \gamma$ where $\alpha , \beta , \gamma \in \mathbb { R } , \gamma \neq 0$ and $i$ is a square root of $- 1$.\\
(B) $\alpha , \alpha , \beta$ where $\alpha , \beta \in \mathbb { R }$ are distinct.\\
(C) $\alpha , \beta , \gamma$ where $\alpha , \beta , \gamma \in \mathbb { R }$ are all distinct.\\
(D) $\alpha , \alpha , \alpha$ for some $\alpha \in \mathbb { R }$.