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Jee Main 2025Medium JEE math MCQ

If the set of all \( a \in \mathbb{R} \), for which the equation \( 2x^2 + (a - 5)x + 15 = 3a \) has no real root, is the interval \((\alpha, \beta)\), and \( X = \{x \in \mathbb{Z} : \alpha < x < \beta\} \), then \( \sum_{x \in X} x^2 \) is equal to
  1. A. 2109
  2. B. 2129
  3. C. 2119
  4. D. 2139

Solution

The correct option is **D**. (D. 2139)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
If the set of all aR a \in \mathbb{R} , for which the equation 2x2+(a5)x+15=3a 2x^2 + (a - 5)x + 15 = 3a has no real root, is the interval (α,β)(\alpha, \beta), and X={xZ:α<x<β} X = \{x \in \mathbb{Z} : \alpha < x < \beta\} , then xXx2 \sum_{x \in X} x^2 is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep