0

0/1

2 Gleichungen

0/1/4

2.4 Ungleichungen

0/1/4/2

2.4.2 Bestimmen der Lösungen

0/1/4/2/1 .
Beispiel 2 - 14
(x - 5) ⋅ (x - 3) ⋅ (x - 2) ⋅ x ⋅ (x - 1) ≥ 0 oder .
x5 - 11 * x4 + 41 * x3 - 61 * x2 + 30 * x ≥ 0 .

PIC .

Abbildung 1: x5 - 11 * x4 + 41 * x3 - 61 * x2 + 30 * x

.

Die Nullstellen sind: 5, 3, 2, 0,-1. .
Wählt man nun für x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F4@  beispielsweise die Werte  −2,  −0.5,   1,   2.5,  4,  6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaey OeI0IaaGOmaiaacYcacaaMc8UaaGPaVlabgkHiTiaaicdacaGGUaGa aGynaiaacYcacaaMc8UaaGPaVlaaykW7caaIXaGaaiilaiaaykW7ca aMc8UaaGPaVlaaikdacaGGUaGaaGynaiaacYcacaaMc8UaaGPaVlaa isdacaGGSaGaaGPaVlaaykW7caaI2aaaaa@5618@ so erkennt man schnell die Intervalle und deren (Tel)Wertebereiche: .
  1. −∞<x≤−1 : f( x )≤0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaey OhIuQaeyipaWJaamiEaiabgsMiJkabgkHiTiaaigdacaaMc8UaaiOo aiaaykW7caWGMbWaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyizIm QaaGimaaaa@4767@ . .
  2. −1<x≤0 : f( x )≥0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0IaaG ymaiabgYda8iaadIhacqGHKjYOcaaIWaGaaGPaVlaacQdacaaMc8Ua amOzamaabmaabaGaamiEaaGaayjkaiaawMcaaabaaaaaaaaapeGaey yzImRaaGimaaaa@45F4@
  3. 0<x≤2 : f( x )≤0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiabgY da8iaadIhacqGHKjYOcaaIYaGaaGPaVlaacQdacaaMc8UaamOzamaa bmaabaGaamiEaaGaayjkaiaawMcaaiabgsMiJkaaicdaaaa@44D7@
  4. 2<x≤3 : f( x )≥0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiabgY da8iaadIhacqGHKjYOcaaIZaGaaGPaVlaacQdacaaMc8UaamOzamaa bmaabaGaamiEaaGaayjkaiaawMcaaabaaaaaaaaapeGaeyyzImRaaG imaaaa@450B@
  5. 3<x≤5 : f( x )≤0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIZaGaeyipaWJaamiEaiabgsMiJkaaiwdacaaMc8UaaiOoaiaa ykW7caWGMbWaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyizImQaaG imaaaa@44FD@
  6. 5<x<∞ : f( x )>0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiabgY da8iaadIhacqGH8aapcqGHEisPcaaMc8UaaiOoaiaaykW7caWGMbWa aeWaaeaacaWG4baacaGLOaGaayzkaaGaeyOpa4JaaGimaaaa@4433@
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