Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?

$I$. It has at least one negative root.

$II$. It has at least one positive root.

$III$. Both its roots are real.

  • [KVPY 2013]
  • A

    $I$ and $II$ only

  • B

    $I$ and $III$ only

  • C

    $II$ and $III$ only

  • D

    All of them

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