MathematicsThe solutions of x for which the following quadratic equation holds 12abx2-9a2-8b2x-6ab=0 are

The solutions of x for which the following quadratic equation holds


 12abx2-9a2-8b2x-6ab=0 are


  1. A
    34b ,2b3a
  2. B
    34b ,-2b3a
  3. C
    -34b ,2b3a
  4. D
    None of these  

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    Solution:

    Given equation: 12abx2-9a2-8b2x-6ab=0 On comparing the given equation with ax2+bx+c=0, we get
    a = 12ab, b = -9a2-8b2 and c = -6ab
    By quadratic formula, we have
    x=-b±b2-4ac2a
    x=-[-9a2-8b2]±[-9a2-8b2]2-4(12ab)(-6ab)2(12ab)
    x=9a2-8b2±81a2+64b2-144a2b2+288a2b22(12ab)
    x=9a2-8b2±81a2+64b2+144a2b22(12ab)
    x=9a2-8b2±[9a2+8b2]22(12ab)
    x=9a2-8b2±9a2+8b22(12ab)
    x=9a2-8b2±9a2+8b22(12ab)
    x=9a2 - 8b2 + 9a2 + 8b22(12ab) and x=9a2 - 8b2 - 9a2 + 8b22(12ab)
    x=18a2 24ab and x=-16b224ab
    x=34b and x=-2b3a
    Therefore, 2 is the correct option.
     
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