2 szkoły ponadpodstawowej

II liceum

II technikum

Matematyka i przykłady jej zastosowań 2. Zakres podstawowy i rozszerzony

a)   W(3)=81   31​⋅3n=81   ∣⋅3   3n=243

a) W(x)=(x3+4)2=(x3)2+2⋅x3⋅4+42=x6+8x3+16

<table style="width:702px;border-collapse:collapse;background-color:#dcdcdc;height:30px;" border="0"> <tbody> <tr> <td style="width:698.011px;">Suma współczynników wielomianu W(x)=anxn+an-1xn-1+...+a1x+a0 jest równa W(1).</td> </tr> </tbody> </table>

a) W(−1)=2⋅(−1)3−3⋅(−1)2+21=2⋅(−1)−3⋅1+21=−2−3+21=16

a) W(0)=2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​⋅0−0+2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​⋅0−6=−6

(1) Wielomian stopnia trzeciego jest postaci: W(x)=a3​x3+a2​x2+a1​x+a0​   Chcemy wskazać

<table style="width:702px;border-collapse:collapse;background-color:#dcdcdc;height:30px;" border="0"> <tbody> <tr> <td style="width:698.011px;">Suma współczynników wielomianu W(x)=anxn+an-1xn-1+...+a1x+a0 jest równa W(1).</td> </tr> </tbody> </table> <hr> a) W(1)=8⋅16−2⋅15+4−10=8−2+4−10=0 &nbsp;

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