"UNIVERSIDAD NACIONAL DEL CENTRO DEL PERU"FACULTAD DE INGENIERA QUMICADEPARTAMENTO ACADEMICO DE QUMICA, INGENIERIA Y TECNOLOGACTEDRA: MTODOS NUMRICOSCATEDRTICO : ING. WILDER EUFRACIO ARIASALUMNA: LUCERO QUISPE MEZASEMESTRE: IV

A. Hallar las races reales y complejas del siguiente polinomio:

f(x)= 2x5-6x4+x3-5x2-4x+12

i)Graficamos la ecuacin:xf(x)

-6-23688

-5-10218

-4-3700

-3-1020

-2-168

-12

012

10

2-40

3-18

4492

52492

67800

719290

841132

ii)Tomamos como puntos iniciales x0=-1; x1=1; x2=3i) Hallando la primera raiz

a5a4a3a2a1a0x

2-61-5-412-1,046512

-1-28-914-10

2-89-14102

-1-210-1933

2-1019-3343

a5a4a3a2a1a0x

2-61-5-412-1,043607

-1,046512-2,0930238,4694429-9,90988215,60337-12,1431

2-8,0930239,4694429-14,9098811,60337-0,14306

-1,046512-2,09302310,659816-21,065537,64866

2-10,1860520,129259-35,9753949,25202

a5a4a3a2a1a0x

2-61-5-412-1,043595

-1,043607-2,0872148,4398736-9,85151915,49915-12,0006

2-8,0872149,4398736-14,8515211,49915-0,00059

-1,043607-2,08721410,618105-20,9326537,34461

2-10,1744320,057979-35,7841748,84376

a5a4a3a2a1a0x

2-61-5-412-1,043595

-1,043595-2,087198,43975-9,85127515,49871-12primera raiz encontrada

2-8,087199,43975-14,8512711,49871-1E-08

-1,043595-2,0871910,617931-20,9320937,34334

2-10,1743820,057681-35,7833748,84206

ii) Obtenemos el polinomio de menor grado:

f(x)=2(x^4)-8,08718979(x^3)+9,3975(x^2)-1,851249x+11,4987

Hallamos la segunda raz

a4a3a2a1a0x

2-8,087189799,43975-14,851274911,49871471

12-6,087189793,352560205-11,4987147segunda raiz encontrada

2-6,087189793,35256021-11,49871475,0626E-09

12-4,08718979-0,73462959

2-4,08718979-0,73462959-12,2333443

ii) Obtenemos el polinomio de menor grado:

f(x)=2(x^3)-6,08718979(x^2)+3,35256021x-11,498717

Hallamos la segunda raz

a3a2a1a0x

2-6,087189793,35256021-11,49871473,1069

36-0,261569389,272972472

2-0,087189793,09099082-2,22574225

3617,738430662,48826433

25,9128102120,8294214

a3a2a1a0x

2-6,087189793,35256021-11,49871473,1009

3,1068566,213711380,3930843311,63717703

20,126521593,745644530,138462309

3,1068566,2137113819,698188972,83660738

26,3402329823,4438334

a3a2a1a0x

2-6,087189793,35256021-11,49871473,1009

3,100956,201899130,3557078511,49915222

20,114709333,708268060,000437499

3,100956,2018991319,587484272,23895292

26,3166084623,2957523

a3a2a1a0x

2-6,087189793,35256021-11,49871473,1009

3,1009316,201861570,3555892311,49871473tercera raiz encontrada

20,114671773,708149434,41522E-09

3,1009316,2018615719,587132772,23705737

26,3165333423,2952821