Verified Solution • 2025–26 Session moderate

QJEEM20Ma5665: JEE Main 2020 Mathematics - Class 11 JEEM20Ma5665 Solution: The product of the roots of the equation 9x 2 - 18

The product of the roots of the
equation 9x2 - 18|x| + 5 = 0 is :

Multiple Choice Options

  • A 59{{5} \over {9}}
  • B 527{{5} \over {27}}
  • C 2581{{25} \over {81}}
  • D 259{{25} \over {9}}

Step-by-Step Verified Solution

9x2−18∣x∣+5=09{x^2} - 18\left| x \right| + 5 = 0

⇒\Rightarrow 9x2−15∣x∣−3∣x∣+5=09{x^2} - 15\left| x \right| - 3\left| x \right| + 5 = 0 ( ∵\because x2 = ∣x∣2{\left| x \right|^2} )

⇒\Rightarrow 3∣x∣(3∣x∣−5)−(3∣x∣−5)=03\left| x \right|(3\left| x \right| - 5) - (3\left| x \right| - 5) = 0

⇒\Rightarrow ∣x∣=13, 53\left| x \right| = {1 \over 3},\,{5 \over 3}

⇒\Rightarrow x=±13,± 53x = \pm {1 \over 3}, \pm \,{5 \over 3}

∴\therefore Product of roots

= (13)(−13)(53)(−53)\left( \frac{1}{3} \right) \left( -\frac{1}{3} \right) \left( \frac{5}{3} \right) \left( -\frac{5}{3} \right) = 2581{{25} \over {81}}

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