4. Oblicz pierwiastki wielomianu: a) W(x) = x3 + 2x2 – 5x – 10 b) Q(x) = x3 – 3x2 – 2x + 6

a) x3 + 2x2 - 5x -10 = 0    x2(x + 2) - 5(x + 2) = 0    (x2 - 5)(x+2) = 0    (x - √5)(x + √5)(x+2) = 0    x = √5 lub x = -√5 lub x = -2 b) x3 - 3x2 - 2x + 6 = 0    x2(x - 3) -2(x - 3) = 0   (x2 - 2)(x - 3) = 0   (x - √2)(x + √2)(x - 3) = 0   x = √2 lub x = -√2 lub x = 3

[latex]a) \\W(x) = x^3 + 2x^2 -5x - 10 \\x^3 + 2x^2 - 5x -10 =0\\x^2(x + 2) -5(x +2 )=0\\(x+2)(x^2-5)=0\\(x+2)(x -sqrt{5})(x +sqrt{5})=0\\x+2=0 vee x -sqrt{5}=0 vee x +sqrt{5}=0\\x=-2 vee x=sqrt{5} vee x =-sqrt{5} [/latex] [latex] b)\\ Q(x) = x^3- 3x^2 - 2x + 6\\x^3 - 3x^2 -2x + 6=0\\x^2(x -3)- 2(x -3)=0\\(x-3)(x^2-2)=0\\(x-3)(x-sqrt{2})(x+sqrt{2})=0\\ x-3=0 vee x-sqrt{2}=0 vee x+sqrt{2} =0\\ x=3 vee x=sqrt{2} vee x=-sqrt{2} [/latex]

oblicz pierwiastki wielomianu 1)W(x)=(2x+3)(2x2-5) 2)R(x)=x2-3x2-4x+12

oblicz pierwiastki wielomianu 1)W(x)=(2x+3)(2x2-5) 2)R(x)=x2-3x2-4x+12...