Q74 / 200 · Manipal (MET) 2010 · Mathematics

If $a, b, c$ are three distinct positive real numbers of real roots of $a x^2+2 b|x|-c=0$ is

  • A
    4
  • Correct answer
    B
    2
  • C
    0
  • D
    None of these

Solution

$a x^2+2 b|x|-c=0$ $\Rightarrow a|x|^2+2 b|x|-c=0$ $\therefore|x|=\frac{-2 b \pm \sqrt{4 b^2+4 a c}}{2}=-b \pm \sqrt{b^2+a c}$ Since, $a, b, c$ are positive. So, $|x|=-b+\sqrt{b^2+a c}$ $\therefore x$ has two real values, neglecting $|x|=-b-\sqrt{b^2+a c}, \text { as }|x|\gt0$

Hence, the correct answer is option: 'B'.

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