Question

Wyznacz współczynniki a,b wielomianu w, jeśli:

a) w(x)= -3x³ + ax²+bx + b i w(-1)=4, w(2)=20

Answer 1

W(x) = - 3 x^3 + a x^2 + b x + b

W(-1) = 4   i    W(2 ) = 20

zatem

-3*(-1)^3 + a*(-1)^2 + b*(-1) + b = 4

- 3*2^3 + a*2^2 +  b*2 + b = 20

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3 + a - b + b = 4

- 24  + 4 a +  3 b = 20

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a = 4 - 3 = 1

- 24 + 4 +  3b = 20

3 b = 40

b = 13  1/3

Odp. a = 1  ,  b = 13  1/3

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