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JEE Main 20204 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2020 · 4 September · Morning Shift · Mathematics · Quadratic Equation

Let [t] denote the greatest integer ≤ t . Then the equation in x,...

Let [t]\left[t\right] denote the greatest integer≤t\le t. Then the equation in x,[x]2+2[x+2]−7=0x, {\left[x\right]}^{2} + 2\left[x + 2\right] - 7 = 0 has :

Options

  1. Aexactly two solutions
  2. Bexactly four integral solutions
  3. Cno integral solution
  4. Dinfinitely many solutions

Correct answer

D. infinitely many solutions

Step-by-step solution

[x]2+2[x+2]−7=0{\left[x\right]}^{2} + 2\left[x + 2\right] - 7 = 0

[x]2+2([x]+2)−7=0{\left[x\right]}^{2} + 2\left(\left[x\right] + 2\right) - 7 = 0

Let \left[x\right] = t</p><p></p><p>{t}^{2} + 2t - 3 = 0</p><p></p><p>t = 1, - 3</p><p>[x]=−3,1</p><p>\left[x\right] = - 3, 1

x∈[−3,−2)∪[1,2)x \in \left[- 3, - 2\right) \cup \left[1, 2\right)

Hence, equation has infinitely many solutions.

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