Let t denote the greatest integer ≤ t . Then the equation in x ,   x 2 + 2 x + 2 - 7 = 0 has :

Let t denote the greatest integer≤t. Then the equation in x, x2+2x+2-7=0 has :
  1. exactly two solutions
  2. exactly four integral solutions
  3. no integral solution
  4. infinitely many solutions

Solution

x2+2x+2−7=0

x2+2x+2−7=0

Let x=t

t2+2t−3=0

t=1, −3

x=-3, 1

x∈−3, −2∪1, 2

Hence, equation has infinitely many solutions.

Asked in: JEE Main 2020 (04 Sep Shift 1)

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