Odpowiedź:
[tex]\huge\boxed{~~a=3~~}[/tex]
Szczegółowe wyjaśnienie:
[tex]W(x)=x^{5} +ax^{4} +3x-10\\\\W(x)~~jest~~podzielny~~przez~~dwumian ~~(x+2)~~\Rightarrow ~~\huge\boxed {~~W(-2)=0~~}\\\\W(-2)=(-2)^5+a(-2)^4+3\cdot (-2)-10\\\\W(-2)=-32+16a-6-10\\\\W(-2)=-48+16a\\\\\\W(-2)=-48+16a~~\land ~~W(-2)=0\\\\~~~~~~~~~~~~~~~~\Downarrow \\\\-48+16a=0\\\\16a=48~~\mid \div 16\\\\\huge\boxed {~~a=3~~}[/tex]
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Odpowiedź:
[tex]\huge\boxed{~~a=3~~}[/tex]
Szczegółowe wyjaśnienie:
Dla przypomnienia:
Rozwiązujemy:
[tex]W(x)=x^{5} +ax^{4} +3x-10\\\\W(x)~~jest~~podzielny~~przez~~dwumian ~~(x+2)~~\Rightarrow ~~\huge\boxed {~~W(-2)=0~~}\\\\W(-2)=(-2)^5+a(-2)^4+3\cdot (-2)-10\\\\W(-2)=-32+16a-6-10\\\\W(-2)=-48+16a\\\\\\W(-2)=-48+16a~~\land ~~W(-2)=0\\\\~~~~~~~~~~~~~~~~\Downarrow \\\\-48+16a=0\\\\16a=48~~\mid \div 16\\\\\huge\boxed {~~a=3~~}[/tex]