W(x)= x^3+ ax^2 + bx + 64
x_2=-2x_1
x_3=4x_1
W(x)=(x-x_1)(x-x_2)(x-x_3)
W(x)= (x-x_1)(x-(-2x_1))(x-4x_1)=(x-x_1)(x+2x_1))(x-4x_1)=
=(x^2+2xx_1-xx_1-2x_1{^2})(x-4x_1)=(x^2+xx_1-2x_1{^2})(x-4x_1)=
=x^3-4x^2x_1+x^2x_1+4xx_1{^2}-2xx_1{^2}+8x_1{^3}=x^3-3x^2x_1-6xx_1{^2}+8x_1{^3}
x^3+ ax^2 + bx + 64 =x^3-3x^2x_1-6xx_1{^2}+8x_1{^3}
ax^2 + bx + 64 = -3x^2x_1 -6xx_1{^2} +8x_1{^3}
8x_1{^3}=64 |/8
x_1{^3}=8
x_1=2
ax^2=-3x^2x_1
a=-3*2
a=-6
bx= -6xx_1{^2}
b=-6*2^2
b=-24
Odpowiedź:
a = -6
b = -24