Parameter-Based Quadratic Tricks in 59 Seconds! 🔥 | JEE Maths
❓ Concept Parameter-Based Quadratic Tricks (α, β) in 59 Sec Whenever you see a quadratic with p, k, λ in coefficients, panic mat karo . 👉 Parameter-based quadratics follow a fixed golden framework — once you apply it step-by-step, answers come automatically. 1️⃣ Quadratic with Parameter General form: a x 2 + b x + c = 0 ax^2 + bx + c = 0 Here, a , b , c depend on a parameter p a,\ b,\ c \quad \text{depend on a parameter } p Roots are: α , β \alpha,\ \beta 👉 Goal in JEE questions: Find range of p such that roots satisfy a given condition. 2️⃣ Real Roots Condition (ALWAYS STEP 1) For real roots: D = b 2 − 4 a c ≥ 0 D = b^2 - 4ac \ge 0 📌 This step is non-negotiable . Most students forget it and lose marks. 👉 Solve: b 2 − 4 a c ≥ 0 ⇒ range of p b^2 - 4ac \ge 0 \Rightarrow \text{range of } p 3️⃣ Sign of Roots (α, β) Use standard relations: α + β = − b a , α β = c a \alpha + \beta = -\frac{b}{a}, \quad \...