Question

podane wielomiany rozłóż na czynniki:

a)w(x)=2x⁵ -4x⁴ +x³

b)w(x)=20x⁵ + 14x⁴ + 2x³

Answer 1

a)

W(x) = 2 x^5 - 4 x^4 + x^3 = x^3 *(2 x^2 - 4 x + 1) =

= 2*( x - 1 + 0,5 p(2))*( x - 1 - 0,5 p(2))* x^3

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bo

delta = (- 4)^2 - 4*2*1 = 16 - 8 = 8

p(delty) = p (8) = 2 p(2)

x = [ 4 - 2p(2)]/4 = 1 - 0,5 p(2)

lub

x = [ 4 + 2 p(2)]/4 =1 + 0,5 p(2)

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b)

W(x) = 20 x^5 + 14 x^4 + 2 x^3 = 2 x^3 * ( 10 x^2 + 7 x + 1) =

= 10*(x + 0,5)*(x + 0,2)* 2 x^3 = 20 x^3 *(x + 0,5)*(x + 0,2)

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bo

delta = 7^2 - 4*10*1 = 49 - 40 = 9

p(delty) = 3

x = [ - 7 - 3 ]/20 = - 10/20 = - 0,5

lub

x =[ - 7 + 3] /20 = - 4/20 = - 0,2

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