JEE Main20231 Feb 2023Morning ShiftMathematicsQuadratic EquationActual
Let S = x : x ∈ ℝ and 3 + 2 x 2 - 4 + 3 - 2 x 2 - 4 = 10 . Then n S is equal to
Options
- A2
- B4
- C6
- D0
Correct answer
B. 4
Step-by-step solution
Given: S = x : 3 + 2 x 2 - 4 + 3 - 2 x 2 - 4 = 10 Now, 3 - 2 = 3 + 2 3 - 2 3 + 2 = 1 3 + 2 So, 3 + 2 x 2 - 4 + 3 - 2 x 2 - 4 = 10 ⇒ 3 + 2 x 2 - 4 + 1 3 + 2 x 2 - 4 = 10 Put 3 + 2 x 2 - 4 = u , then u + 1 u = 10 ⇒ u 2 - 10 u + 1 = 0 ⇒ u = 10 ± 100 - 4 2 ⇒ u = 5 ± 24 ⇒ u = 5 ± 2 3 2 ⇒ u = 3 ± 2 2 ⇒ 3 + 2 x 2 - 4 = 3 ± 2 2 So, 3 + 2 x 2 - 4 = 3 + 2 2 and 3 + 2 x 2 - 4 = 1 3 + 2 2 Therefore, x 2 - 4 = 2   &   x 2 - 4 = - 2 ⇒ x =