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CLASE 9

CLASE 9. Resolución de ecuaciones en. C. Resuelve:. x 3 + 2x 2 + 2x + 1 = 0. Divisores de 1: 1 y – 1. 1 2 2 1. -1. -1. -1. -1. 1. 1. 1. 0. x 3 +2x 2 +2x+1=(x+1)(x 2 +x+1). Veamos:. x 3 +2x 2 +2x+1=(x+1)(x 2 +x+1).

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CLASE 9

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  1. CLASE 9

  2. Resolución de ecuaciones en C

  3. Resuelve: x3 + 2x2 + 2x + 1 = 0 Divisores de 1: 1 y –1 1 2 2 1 . -1 -1 -1 -1 1 1 1 0 x3+2x2+2x+1=(x+1)(x2+x+1)

  4. Veamos: x3+2x2+2x+1=(x+1)(x2+x+1) x2+x+1 no tiene descomposición en . D = b2 – 4ac a = 1 . b = 1 D = 12 – 4.1.1 c = 1 D = – 3

  5. x3+2x2+2x+1=(x+1)(x2+x+1) D = – 3 ;

  6. 2 3 = 3i 2 i= 1 x3+2x2+2x+1=(x+1)(x2+x+1) Como

  7. Por tanto: X= – 1

  8. Toda ecuación de grado n en C tiene exactamente n raíces complejas. Teorema fundamental del Álgebra

  9. Resuelve en : x = C x = x4 + 2x2 +1 = 0 (x2 +1)2 = 0 x2 +1 = 0 x1,2 = i x2 = –1 x3,4 = –i

  10. Resuelve en : C ESTUDIO INDIVIDUAL a) x3 – 2x2 – 9 = 0 x3= 3 b) y2 – 2y – 5 = 0 x1= 1 + 2i x2= 1 –2i

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