Question

Wielomiany. Rozwiąż 1. x3+5x2+2x-8=0 2. x5-x4-5x3+5x2+6x-6=0 3. x3-x2+4x-4=0 4. 2x3-3x2+6x-5=0 5. x3-2x2+3x-2=0

Answer 1

1. x3 + 5x2 + 2x - 8 = 0

W (1) = 0

 

schemat HORNERA:

1 5 2 -8

1  1 6  8

1 6 8  0

 

(x-1)(x2 + 6x + 8) = 0

delta = 36 - 32 = 4; pierwiastek z delty = 2

 

x1 = (-6-2)/2 = -4

x2 = (-6 + 2)/2 = -2

(x-1)(x+4)(x+2) = 0

x=1 lub x=-4 lub x=-2

 

3.

x3-x2+4x-4 = 0

x2(x-1) + 4(x-1) = 0

(x2 +4)(x-1) = 0

x=1