JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If the set of all \(\mathrm{a} \in \mathrm{R}-\{1\}\), 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 _______ .
- A 2
- B 5
- C 7
- D 9
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
Both the roots are positive \(\begin{aligned} & D \geq 0 \\ & 4(a-3)^2-4 \times 9(1-a) \geq 0 \\ & a^2-6 a+9-9+9 a \geq 0 \\ & a^2+3 a \geq 0 \\ & a(a+3) \geq 0 \end{aligned}\) \(\mathrm{a} \in(-\infty,-3] \cup[0, \infty)\) ...(i)…
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