What must be added to $3x^{2} - 5x + 4$ to get $7x^{2} + 2x - 1$?

What must be added to $3x^{2} - 5x + 4$ to get $7x^{2} + 2x - 1$?
  1. $4x^{2} - 7x - 5$
  2. $4x^{2} + 7x - 5$
  3. $10x^{2} + 7x + 3$
  4. $4x^{2} - 3x + 5$

Solution

Required = $(7x^{2} + 2x - 1) - (3x^{2} - 5x + 4) = 4x^{2} + 7x - 5$.

Asked in: IMO

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