wielomian
: 16 mar 2010, 09:26
dany jest wielomian W(x)=3x^3-2x^2-5x+1
Oblicz
W(-1)-3W(0)
---------------- =
W (pierwiastek z 2)
Oblicz
W(-1)-3W(0)
---------------- =
W (pierwiastek z 2)
\(W(-1)=3\cdot(-1)^3-2\cdot(-1)^2-5\cdot(-1)+1=-3-2+5+1=1\\W(0)=3\cdot0-2\cdot0-5\cdot0+1=1\\W(\sqrt{2})=3\cdot(\sqrt{2})^3-2\cdot(\sqrt{2})^2-5\cdot\sqrt{2}+1=3\cdot2\sqrt{2}-2\cdot2-5\sqrt{2}+1=6\sqrt{2}-4-5\sqrt{2}+1=\sqrt{2}-3\)
\(\frac{W(-1)-3W(0)}{W(\sqrt{2})}=\frac{1-3\cdot1}{\sqrt{2}-3}=\frac{-3}{\sqrt{2}-3}\cdot\frac{\sqrt{2}+3}{\sqrt{2}+3}=\frac{-3\sqrt{2}-9}{2-3}=3\sqrt{2}+9\)