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Quadratic Equation and Inequalities question

2025 · 2 Apr · Shift 2 · Q47

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JEE Main
Mathematics
Quadratic Equation and Inequalities
2025 · 2 Apr · Shift 2 · Q47

Quadratic Equation and Inequalities question

2025 · 2 Apr · Shift 2 · Q47

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1

If the set of all

\mathrm{a} \in \mathbf{R}-\{1\}

, for which the roots of the equation

(1-\mathrm{a}) x^2+2(\mathrm{a}-3) x+9=0

are positive is

(-\infty,-\alpha] \cup[\beta, \gamma)

, then

2 \alpha+\beta+\gamma

is equal to

\qquad

.

Numerical answer

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