The equation whose roots are the square of the roots of the equation 2×2+3x+1=0

The equation whose roots are the square of the roots of the equation 2x2+3x+1=0

  1. A

    4x2+5x+1=0

  2. B

    4x2x+1=0

  3. C

    4x25x1=0

  4. D

    4x25x+1=0

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    Solution:

    Let the roots of equation
    2x2+3x+1=0 is α and β
    Then ,α+β=32 and αβ=12
     α2+β2=(α+β)22αβ=3222×12=941=54
    and α2β2=122=14
     Required equation is
    x2α2+β2x+α2β2=0 x254x+14=0 4x25x+1=0

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