Arithmetic and Geometric Progressions

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Type of Progression

Type of Progression

    If the equation px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common root, then in which type of progression is
    1. are in G.P
    2. are in A.P
    3. are in H.P
    4. Insufficient Data


  • Correct Answer
    Choice B. are in A.P

Detailed Solution

Since p,q,r are in G.P. we have q2 = pr. On solving px2 +2qx +r = 0 we get

x =

=) x = (q2 = pr)

=) x =

Thus x = is the repeated root of px2+2qx+r = 0

∴ x = is also a root of dx2+2ex+f = 0

=) d.


=) dq2 - 2eqp + fp2 = 0

=) [On dividing by pq2]



Hence it can be clearly seen that are in A.P

Correct Answer: are in A.P

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More questions from Progressions

  1. Counting and Progressions
  2. Common Ratio
  3. Common Difference
  4. Sum up to 'n' Terms
  5. AP Puzzle
  6. GP Logical Puzzle
With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.