If the set of all a R, for which the equation 2x²+(a-5)x+15=3a has no real root, is the interval (α, β), and X= Z: α < x < β, then Σ x X x² is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q133

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

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: