Aproximación de raíces por bisección (1 de 2)

Parte 1: Aproximación manual
[list=1][*]Elige un polinomio de grado 5 que tenga una raíz real positiva, modificando la fórmula: [img]http://latex.codecogs.com/png.latex?%5Cdpi%7B150%7D%20a_5%20x%5E5++a_4%20x%5E4+a_3%20x%5E3+a_2%20x%5E2+a_1%20x+a_0[/img][br][b]a_5 debe ser distinto de cero[/b][br][/*][*]Se aproximará el valor de esa raíz positiva [i]r [/i]con 4 decimales.[br][/*][*]Llena la tabla con los valores de[i] a, b[/i] y [i]r[/i] de cada [i]iteración [/i]del método de bisección.[/*][*]Itera el método hasta que se cumpla p(r)<.0001[/*][/list][br]
Escribe el polinomio que elegiste y el valor de la raíz aproximada
Parte 2: Automático de uno en uno (Usar el applet de abajo)
1. Presiona el botón [Cambiar Polinomio] hasta obtener un polinomio con al menos dos raíces reales.[br][br]2. Ubica en la gráfica una posible raíz, [b]r[/b], anota el valor que parece tener en la barra de entrada[br](si parece estar en 0.5)[br] r=0.5[br]2. Comprueba si r es raíz, evaluando p en r:[br]pr=p(r)[br] si [b]pr[/b]=0, encontraste la raíz exacta[br]2. Crea un número [b]a [/b]cercano y la izquierda de la posible raíz[br](si la posible raíz es 0.5)[br] a=0.4 [br]3. Para ver el número en la vista gráfica, crea el punto en el eje X[br] A=(a,0)[br]4. Crea un número [b]b [/b]cercano y la derecha de la posible raíz[br](si la posible raíz es 0.5)[br] b=0.6[br]5. Para ver el número en la vista gráfica, crea el punto en el eje X[br] B=(b,0)[br]6. Comprueba que hay una raíz entre esos dos números, comparando el signo del polinomio en ellos[br] sa= sgn(p(a))[br] sb= sgn(p(b))[br] sr= sgn(p(r))[br]7. Crea un botón [icon]/images/ggb/toolbar/mode_buttonaction.png[/icon]para que GeoGebra calcule la bisección del intervalo (a, b) y decida en qué lado está la raíz[br][br]Ingresa las siguientes líneas en el [i]script [/i]del botón[br][br][img]data:image/png;base64,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[/img]
Escribe el polinomio que obtuviste
¿Cuántos clicks se necesitan para que el valor de pr<0.0001 (sin contar el signo)?
Cuál es el valor final de r?
Prueba que el botón funcione para aproximar otra raíz del mismo polinomio, escribe aquí:[br]a)primera aproximación de la nueva raíz[br]b)cantidad de clicks para llegar a la raíz con p(r)<.0001[br]

Aproximación de raíces por bisección (2 de 2)

Parte 1: Bisección repetida k veces
Sobre la construcción anterior, se añadirán nuevos elementos. Antes de iniciar esta sección, debes tener:[br][list][*]polinomio p(x)[/*][*]números a, b, n, r, sa, sb, sr[/*][*]Puntos A, B, R[/*][*]Botón para bisección manual, un paso a la vez[br][/*][/list]Crearemos un botón que aplique la misma acción, pero ahora K veces.[br]1. Crea un número entero, k, con un valor entero relativamente alto[br]  k=50[br]2. Crea un segundo botón para que GeoGebra aplique las instrucciones del primer botón k veces, con el guión[br] Repite(k, EjecutaAlClic(botón1))[br]El primer botón debe llevar de nombre "botón1"[br]
Según la fórmula
¿Cuál debería ser la raíz diferente de cero?
¿A las cuántas repeticiones se obtendría el valor exacto de pi?
comprobar el funcionamiento de la construcción
1. Redefine el polinomio p con la siguiente entrada:[br] p(x)= x^5+4x^4+x^3-10x^2-4x+8
2. ¿Cuál es el valor de la raíz negativa?[br]¿Cuántos clicks se necesitaron para aproximar la raíz?
3. Vuelve a aproximar la raíz negativa con valores iniciales de [br]a=-3[br]b=0[br]¿Por qué crees que geogebra deja de aproximar el valor de la raíz antes de llegar a r=2?
4. Intenta aproximar la raíz positiva[br]¿Describe qué pasa cuando usas el botón?
5. ¿Por qué crees que este método sólo encuentra raíces de multiplicidad impar?
Parte 2: Cálculo de raíces pares
Para calcular las raíces de multiplicidad par, hay que complementar la construcción usando la relación entre un polinomio y su derivada.[br]Si [i]r[/i] es una raíz de multiplicidad par de [i]p(x)[/i], entonces también es raíz de la derivada [i]p'(x).[/i]
¿Las raíces pares de p(x), son pares o impares de p'(x)?
Usando la respuesta anterior, si encontramos las raíces impares de[i] p'(x)[/i] estaríamos encontrando las raíces pares de [i]p(x)[/i].[br]Crearemos un segundo botón para aproximar estas otras raíces, pero primero:[br][br][list=1][*]Crea la derivada de p, escribiendo directamente en la barra de entrada:[br]p'[br][/*][*]Crea los números equivalentes a los signos de [i]a, b [/i]y [i]r,[/i] para [i]p'(x):[br]sa2= sgn(p'(a))[br]sb2= sgn(p'(b))[br]sr2= sgn(p'(r))[br][/i][/*][*]Crea el nuevo botón para aproximar raíces pares, con el guión: [br]Valor[r,(a+b)/2][br]Si[sa2==sr2, Valor[a,r]][br]Si[sb2==sr2, Valor[b,r]][br][/*][/list]Este tercer botón, por default se llamará [i]botón3[br][/i]Ahora puedes crear un cuarto botón que aplique K repeticiones del [i]botón3[br] [/i] 4. Crea el botón [i]k bisecciones pares[/i] con el siguiente guión:[br]   Repite(k, EjecutaAlClic(botón3))
5. ¿Este polinomio p(x) tiene raíces complejas?[br]Explica por qué
6. ¿Cuál es la fórmula factorizada del polinomio p?
Parte 3: Comprobación final
El archivo construido hasta este paso te debe permitir aproximar todas las raíces reales positivas y negativas.[br]Para comprobarlo, factoriza (lo más posible) los siguientes polinomios.
1)
p(x)=x^6-0.091x^5 + 2.693x^4+3.006x^3-3.213x^2-2.761x
2)
p(x)=x^6-3.821x^5+9.342x^4-15.218x^3+11.543x^2-1.573x-1.276

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