Question

Wielomiany

Dany jest wielomian W(x) = -x^3 + 2x^2 - 3x

Oblicz:

W (1- pierwiastek z 5)

W (pierwiastek z 2 - pierwiastek z 3)

Answer 1

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

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W(1-√5)=-(1-√5)³+2*(1-√5)²-3(1-√5)

W(1-√5)=-[1-3√5+15-5√5]+2*[1-2√5+5]-3+3√5

W(1-√5)=-1+3√5-15+5√5+2-4√5+1-3+3√5

W(1-√5)=7√5-16

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W(√2-√3)=-(√2-√3)³+2(√2-√3)²-2(√2-√3)

W(√2-√3)=-[2√2-12√3+9√2-3√3]+2*[2-2√6+3]-2√2+2√3

W(√2-√3)=-11√2+15√3+10-4√6-2√2+2√3

W(√2-√3)=-13√2+17√3-4√6+10

Answer 2

w(1-p5)=-(1-p5)^3+2(1-p5)^2-3+3p5=-1+3*p5-3*5-5*p5+2-4*p5+10-3+3p5=10+15-5*p5=23-7*p5
W(p2-p3)=-( p2-p3)^3+2(p2-p3)^2-3(p2-p3)=-2p2+2p3-3p2+3p3+4-4p6+6-3p2+3p3=-8p2+8p3-4p6+10