Important Questions - Monomath

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Quadratic Equations - Important Questions

⚡ 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

1

JEE Standard4 Marks

If one root of x² − 6x + k = 0 is twice the other, find k.

▶ Show Detailed Solution

Let roots be α, 2α.
3α = 6 ⇒ α = 2.
2α² = k ⇒ k = 2(2)² = 8