If the set of all a \in R-\{1\}, for which the roots of the equation (1-a) x^2+2(a-3) x+9=0 are positive is (-\infty,-\alpha] \cup[\beta, \gamma), then 2 \alpha+\beta+\gamma is equal to \_\_\_\_\_ . [2 Apr 2025 Shift 2]

JEE Main 2 Apr 2025 Shift 2 Paper

Section: Mathematics

Question : 22 of 75

Marks: +1, -0

If the set of all a∈R−{1}, for which the roots of the equation (1−a)x2+2(a−3)x+9=0 are positive is (−∞,−α]∪[β,γ), then 2α+β+γ is equal to _____ .

[2 Apr 2025 Shift 2]

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