JEE Main 2024 — Quadratic Equation Question with Solution
JEE Main 2024 (05 Apr Shift 2)
Question
The number of real solutions of the equation is_________
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Show full solutionCorrect answer: 3
Correct answer
3
Step-by-step explanation
Case I :
$\begin{aligned}
& x^2+5 x+2 x+12=0 \\
& x^2+7 x+12=0 \\
& x=-3,-4
\end{aligned}$
Case II :
$\begin{aligned}
& -x^2-3 x+12=0 \\
& x=\frac{-3 \pm \sqrt{9+48}}{2} \\
& =\frac{-3 \pm \sqrt{57}}{2} \\
& x=\frac{-3-\sqrt{57}}{2}, \frac{-3+\sqrt{57}}{2} \text { (rejected) }
\end{aligned}$
Case III :
$\begin{aligned}
& -x^2-5 x-2 x-14-2=0 \\
& x^2+7 x+16=0 \\
& D=49-64 < 0
\end{aligned}$
No solutions
No. of solutions
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This is a previous-year question from JEE Main 2024, 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.