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Home » "Shockion Own These Rare Blue Hydrangeas—Watch Gardeners Drop Overwith This One! - Appcentric

"Shockion Own These Rare Blue Hydrangeas—Watch Gardeners Drop Overwith This One! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 und \( f(6) = 216 - 288 + 54 - 18 = -36 < 0 \), \( f(5) = 125 - 200 + 45 - 18 = -48 < 0 \), \( f(6.5) \approx 274.6 - 338 + 58.5 - 18 = -24.9 < 0 \), \( f(7) = 343 - 392 + 63 - 18 = 6 > 0 \).

📌 Also liegt eine reelle Wurzel zwischen 6.5 und 7, und da es nur eine positive Extremstelle mit fallendem Verlauf nach oben, und \( f(w) \to \infty \) für \( w \to \infty \), und \( f(w) < 0 \) bei kleinen \( w \), gibt es nur **eine** reelle Wurzel (die andere zwei sind komplex oder negativ).

📌 Prüfe Vorzeichenwechsel: \( f(0) = -18 < 0 \), \( f(1) = 1 - 8 + 9 - 18 = -16 < 0 \), \( f(2) = 8 - 32 + 18 - 18 = -24 < 0 \), \( f(3) = 27 - 72 + 27 - 18 = -36 < 0 \), \( f(4) = 64 - 128 + 36 - 18 = -46 < 0 \), \( f(5) = -48 < 0 \), \( f(6) = -36 < 0 \), \( f(6.7) \approx 302.5 - 360.88 + 60.3 - 18 \approx -16.08 \), \( f(6.9) \approx 328.5 - 383.28 + 62.1 - 18 \approx -0.68 \), \( f(6.95) \approx 334.5 - 388.18 + 62.55 - 18 \approx 0.87 > 0 \).

📌 Also eine reelle Wurzel zwischen 6.9 und 6.95, und da es nur eine reelle Wurzel ist (nach Ableitung und Graphie-Analyse), und zwei komplexe, dann gibt es nur **eine** reelle \( w \), also nur **eine** reelle \( v \).

📌 Aber das widerspricht der Annahme „alle Wurzeln sind reell. Da die Gleichung kubisch ist, müssen entweder drei reelle oder eine reelle und zwei komplexe sein.

📌 Wir müssen prüfen, ob alle Wurzeln \( w_i \) reell sind. Diskriminante eines Kubus \( w^3 + pw + q \): erste Form für \( w^3 + aw^2 + bw + c \), hier:

📌 \( f(w) = w^3 - 8w^2 + 9w - 18 \), also ohne \( w^2 \) bei Transformation? Besser: mache Substitution \( w = z + \frac{8}{3} \).

📌 Sei \( w = z + \frac{8}{3} \), dann:

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