kolejny wielomian z paramtrem

[wirus1910]

Dla jakich wartosci parametru m,a,b wielomiany
\(\displaystyle{ W(x)= (x+2)^{2} (x-m)}\)
\(\displaystyle{ Q(x)= x^{3}+ x^{2}+ax+b}\)
sa rowne.

[Sherlock]

\(\displaystyle{ (x+2)^{2} (x-m)= x^{3}+ x^{2}+ax+b}\)
\(\displaystyle{ (x^2+4x+4)(x-m)=x^{3}+ x^{2}+ax+b}\)
\(\displaystyle{ x^3-mx^2+4x^2-4xm+4x-4m=x^{3}+ x^{2}+ax+b}\)
\(\displaystyle{ x^3+x^2(4-m)+x(4-4m)-4m=x^{3}+ x^{2}+ax+b}\)

\(\displaystyle{ \begin{cases} 4-m=1 \\ 4-4m=a\\b=-4m \end{cases}}\)

[mmoonniiaa]

\(\displaystyle{ W(x)=(x^2+4x+4)(x-m)=x^3-mx^2+4x^2-4mx+4x-4m=x^3+(4-m)x^2+(4-4m)x-4m\\
Q(x)=x^3+x^2+ax+b\\
W(x)=Q(x) \begin{cases} 1=1 \\ 4-m=1 \\ 4-4m=a \\ -4m=b \end{cases} \begin{cases} m=3 \\ a=-8 \\ b=-12 \end{cases}}\)