Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is

  • [KVPY 2011]
  • A

    $9$

  • B

    $18$

  • C

    $24$

  • D

    $30$

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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?

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

$III$. Both its roots are real.

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