JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let the set of all values of \(\mathrm{p} \in \mathbb{R}\), for which both the roots of the equation \(x^2-(p+2) x+(2 p+9)=0\) are negative real numbers, be the interval \((\alpha, \beta]\). Then \(\beta-2 \alpha\) is equal to
- A 0
- B 9
- C 5
- D 20
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
Using location of roots : (i) \(\mathrm{D} \geq 0\) (ii) \(\frac{-\mathrm{b}}{2 \mathrm{a}} \lt 0\) (iii) a. \(\mathrm{f}(0) \gt 0\) \(\begin{aligned} & (p+2)^2-4(2 p+9) \geq 0 \\ & (p+4)(p-8) \geq 0 \quad p+2 \lt 0 \quad 2 p+9 \gt 0 \end{aligned}\) Intersection…
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