Odpowiedź:
a ) W(x) = √2*( x - 4)*(x + 1)*(x - 3)*(x + 3) = 0
x - 4 = 0 lub x + 1 = 0 lub x - 3 = 0 lub x + 3 = 0
x = 4 lub x = - 1 lub x = 3 lub x = - 3
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b )
W( x) = -3 x*(2 x - 5)*(x - √3)*( x + √3)*( x² + 4) = 0
x = 0 lub 2 x - 5 = 0 lub x - √3 = 0 lub x + √3 = 0 x² + 4 > 0
x = 0 lub x = 2,5 lub x = √3 lub x = - √3
==============================================
c )
W( x ) = x²*( 3 x - [tex]\frac{3}{2})*(x^2 - \frac{1}{2} x)*(2 x^2 + 6)[/tex]
W(x) = x³*( 3 x - [tex]\frac{3}{2}[/tex])*(x - [tex]\frac{1}{2})[/tex] = 0 2 [tex]x^{2} + 6 > 0[/tex]
x = 0 lub 3 x - [tex]\frac{3}{2} = 0[/tex] lub x - [tex]\frac{1}{2} = 0[/tex]
x = 0 lub x = [tex]\frac{1}{2}[/tex] - pierwiastek podwójny
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d ) W( x) = x³ -2 x² - 8 x = x*(x² -2 x - 8 ) =x*( x + 2)*(x - 4) = 0
x = 0 lub x + 2 = 0 lub x - 4 = 0
x = 0 lub x = - 2 lub x = 4
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Odpowiedź:
a ) W(x) = √2*( x - 4)*(x + 1)*(x - 3)*(x + 3) = 0
x - 4 = 0 lub x + 1 = 0 lub x - 3 = 0 lub x + 3 = 0
x = 4 lub x = - 1 lub x = 3 lub x = - 3
=======================================
b )
W( x) = -3 x*(2 x - 5)*(x - √3)*( x + √3)*( x² + 4) = 0
x = 0 lub 2 x - 5 = 0 lub x - √3 = 0 lub x + √3 = 0 x² + 4 > 0
x = 0 lub x = 2,5 lub x = √3 lub x = - √3
==============================================
c )
W( x ) = x²*( 3 x - [tex]\frac{3}{2})*(x^2 - \frac{1}{2} x)*(2 x^2 + 6)[/tex]
W(x) = x³*( 3 x - [tex]\frac{3}{2}[/tex])*(x - [tex]\frac{1}{2})[/tex] = 0 2 [tex]x^{2} + 6 > 0[/tex]
x = 0 lub 3 x - [tex]\frac{3}{2} = 0[/tex] lub x - [tex]\frac{1}{2} = 0[/tex]
x = 0 lub x = [tex]\frac{1}{2}[/tex] - pierwiastek podwójny
===============
d ) W( x) = x³ -2 x² - 8 x = x*(x² -2 x - 8 ) =x*( x + 2)*(x - 4) = 0
x = 0 lub x + 2 = 0 lub x - 4 = 0
x = 0 lub x = - 2 lub x = 4
=============================
Szczegółowe wyjaśnienie: