JEE Main Shortcut: Kab Quadratic ke Dono Roots Negative Hote Hain? 💡
❓ Concept Both Roots Negative Trick in 59 Sec Finding when both roots of a quadratic equation are negative is one of the most scoring and repetitive JEE topics . Good news? 👉 It follows just 3 golden rules . 1️⃣ Quadratic Form General quadratic: a x 2 + b x + c = 0 ax^2 + bx + c = 0 First, ensure: a > 0 a > 0 📌 If a < 0 a < 0 , multiply the equation by –1 before applying the rules. 2️⃣ Condition 1 — Roots Must Be Real For real roots: D = b 2 − 4 a c ≥ 0 D = b^2 - 4ac \ge 0 This condition is mandatory . No real roots → no sign discussion. 3️⃣ Condition 2 — Sum of Roots α + β = − b a \alpha + \beta = -\frac{b}{a} For both roots negative : α + β < 0 \alpha + \beta < 0 Since a > 0 a > 0 : − b a < 0 ⇒ b > 0 -\frac{b}{a} < 0 \Rightarrow b > 0 4️⃣ Condition 3 — Product of Roots α β = c a \alpha\beta = \frac{c}{a} For both roots negative : α β > 0 \alpha\beta > 0 Again, since a > 0 a > 0 : c > 0 c > 0 5️⃣...