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The quadratic formula solves any equation ax² + bx + c = 0. The discriminant b²−4ac tells you how many real solutions exist before you solve.
Trin-for-trin guide
- 1Write in standard form: ax² + bx + c = 0
- 2Calculate discriminant: Δ = b² − 4ac
- 3Δ > 0: two real roots; Δ = 0: one root; Δ < 0: complex roots
- 4Apply: x = (−b ± √Δ) / 2a
Løste eksempler
Input
x²−5x+6=0
Resultat
x=3 or x=2
Δ=1>0, two roots
Input
x²−2x+1=0
Resultat
x=1 (repeated)
Δ=0, one root
Input
x²+x+1=0
Resultat
Complex roots
Δ=−3<0