Let the set of all values of p R, for which both the roots of the equation x² - (p + 2)x + (2p + 9) = 0 are negative real numbers, be the interval (α, β]. Then β - 2α is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q189

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

Let the set of all values of

p \in \mathbb{R}

, for which both the roots of the equation

x^2 - (p + 2)x + (2p + 9) = 0

are negative real numbers, be the interval

(\alpha, \beta]

. Then

\beta - 2\alpha

is equal to: