[tex]W(x)=(x^{2} -m)(x^{2} -10x+25)\\\\W(x)=(x^{2} -m )(x^{2} -2\cdot 5\cdot x + 5^{2} )\\\\W(x)=(x^{2} -m )(x-5)^{2} \\\\W(x)=(x^{2} -(\sqrt{m} )^{2} )(x-5)^{2}\\\\W(x)=(x-\sqrt{m} )(x+\sqrt{m} )(x-5)^{2}~~, zal.~~m> 0\\\\Wielomian~~W(x)~~posiada~~trzy~~~~pierwiastki:\\\\x=\sqrt{m} ~~,~~x=-\sqrt{m} ~~,~~x=5~~przy ~~zal.~~m> 0[/tex]
Korzystałam ze wzorów skróconego mnożenia:
[tex](x^{2} -y^{2}) =(x-y)(x+y)\\\\(x-y)^{2} =x^{2} -2\cdotx\cdot y +y^{2}[/tex]
[tex]Odp: Wielonian ~~W(x)~~posiada ~~trzy ~~pierwistki~~ x=5,~~x=\sqrt{m} ,~~x=-\sqrt{m} ~~zal.m>0[/tex]
