JEE Main 2025 — Quadratic Equation Question with Solution
JEE Main 2025 (7 Apr Shift 1)
Question
Let the set of all values of , for which both the roots of the equation are negative real numbers, be the interval . Then is equal to
Choose an option
Show full solutionCorrect option: C
Correct answer
C5
Step-by-step explanation
Using location of roots :
(i)
(ii)
(iii) a.
$\begin{aligned}
& (p+2)^2-4(2 p+9) \geq 0 \\ & (p+4)(p-8) \geq 0 \quad p+2 \lt 0 \quad 2 p+9 \gt 0
\end{aligned}p \in\left(-\frac{9}{2},-4\right]\therefore \beta-2 \alpha=-4+9=5$
(i)
(ii)
(iii) a.
$\begin{aligned}
& (p+2)^2-4(2 p+9) \geq 0 \\ & (p+4)(p-8) \geq 0 \quad p+2 \lt 0 \quad 2 p+9 \gt 0
\end{aligned}p \in\left(-\frac{9}{2},-4\right]\therefore \beta-2 \alpha=-4+9=5$
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This is a previous-year question from JEE Main 2025, covering the Quadratic Equation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.