Question

Wyznacz liczby a i b, żeby wielomian ....

Answer 1

Odpowiedź:

[tex]W(x)=x^{4} +2x^{2} +ax+b\\P(x)=(x-1)(x+2)\\W(1)=0\\W(-2)=0\\W(1)=1+2+a+b=a+b+3\\W(-2)=(-2)^4+2\cdot(-2)^2-2a+b=-2a+b+16+8=-2a+b+24\\\left\{\begin{array}{llc}a+b=-3\\-2a+b=-24/\cdot(-1)\end{array} \right.\\+\underline{\left\{\begin{array}{llc}a+b=-3\\2a-b=24\end{array} \right.}\\3a=21/:3\\a=7\\b=-a-3\\b=-7-3=-10\\\left\{\begin{array}{llc}a=7\\ b=-10\end{array} \right.[/tex]