Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^2-12 x+[x]+31=0$ and $x ^2-5| x +2|-4=0$ respectively, where $[ x ]$ denotes the greatest integer $\leq x$. Then $m ^2+ mn + n ^2$ is equal to $..............$.

  • [JEE MAIN 2023]
  • A

    $9$

  • B

    $8$

  • C

    $7$

  • D

    $6$

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