Question

Dany jest wielomian . Znajdz warości wspolczynników a, b oraz c jesli wiadomo ,że W(0)=1 W(1)=0 W(2)=45 .

Answer 1

W(x)=ax⁴+bx²+c

{W(0)=1

{W(1)=0

{W(2)=45

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{1=a*0⁴+b*0²+c

{0=a*1⁴+b*1²+c

{45=a*2⁴+b*2²+c

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{c=1

{0=a+b+1

{45=16a+4b+1

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{c=1

{a=-1-b

{44=16*(-1-b)+4b

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{c=1

{a=-1-b

{44=-16-16b+4b

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{c=1

{a=-1-b

{-12b=60

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{c=1

{a=-1-b

{b=-5

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{c=1

{a=-1-(-5)

{b=-5

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{c=1

{a=-1+5

{b=-5

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{c=1

{a=4

{b=-5

Wielomian W(x)=4x⁴-5x²+1