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JEE Main 20205 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2020 · 5 September · Morning Shift · Mathematics · Quadratic Equation

The product of the roots of the equation 9 x ^ 2 - 18 | x | + 5 = 0...

The product of the roots of the equation 9x2−18∣x∣+5=09{x}^{2} - 18 | x | + 5 = 0 is :

Options

  1. A59\dfrac{5}{9}
  2. B2581\dfrac{25}{81}
  3. C527\dfrac{5}{27}
  4. D259\dfrac{25}{9}

Correct answer

B. 2581\dfrac{25}{81}

Step-by-step solution

∵x2=∣x∣2∵ {x}^{2} = | x{|}^{2}

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

⇒(3∣x∣−1)(3∣x∣−5)=0⇒ ( 3\left|x\right| - 1 ) ( 3\left|x\right| - 5 ) = 0

⇒∣x∣=13,53⇒ | x | = \dfrac{1}{3}, \dfrac{5}{3}

∴x=13,−13,53,−53∴ x = \dfrac{1}{3}, \dfrac{- 1}{3}, \dfrac{5}{3}, \dfrac{- 5}{3}

product of roots =13(−13)(53)(−53)=2581= \dfrac{1}{3}\left(- \dfrac{1}{3}\right)\left(\dfrac{5}{3}\right)\left(\dfrac{- 5}{3}\right) = \dfrac{25}{81}

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