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Quadratic Equations - Previous Year Questions

⏱️ Est. Revision Time: 15 Mins
⚡ Key Formulas at a Glance
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Nature of Roots
Δ = b² − 4ac: Δ>0 real & distinct, Δ=0 equal, Δ<0 no real roots
Sum of roots
α + β = −b/a
🔍
📅 Year 2024
Q1
JEE Main 2024 Paper 1
If both roots of x² − 2ax + a² + a − 3 = 0 are less than 3, find range of a.
▶ Show Detailed Solution
(1) Δ ≥ 0 ⇒ a ≤ 3.
(2) f(3) > 0 ⇒ a 3.
(3) Vertex < 3 ⇒ a < 3.
Intersection: a < 2