Verified Solution • 2025–26 Session moderate

QJEEM20Ma4c53: JEE Main 2020 Mathematics - Class 11 JEEM20Ma4c53 Solution

If α\alpha and β\beta are the roots of the equation
2x(2x + 1) = 1, then β\beta is equal to :

Multiple Choice Options

  • A −2α(α+1)- 2\alpha \left( {\alpha + 1} \right)
  • B 2α(α+1)2\alpha \left( {\alpha + 1} \right)
  • C 2α22{\alpha ^2}
  • D 2α(α−1)2\alpha \left( {\alpha - 1} \right)

Step-by-Step Verified Solution

α\alpha and β\beta are the roots of the equation
4x2 + 2x – 1 = 0.

∴\therefore α\alpha + β\beta = −12- {1 \over 2}

⇒\Rightarrow -1 = 2 α\alpha + 2 β\beta

and 4 α\alpha 2 + 2 α\alpha - 1 = 0

⇒\Rightarrow 4 α\alpha 2 + 2 α\alpha + 2 α\alpha + 2 β\beta = 0

⇒\Rightarrow β\beta = −2α(α+1)- 2\alpha \left( {\alpha + 1} \right)

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