znajdz miejsce zerowe funkcji f danej wzorem : a) f(x)=6(1-x²)-3(2x²)-2

[latex]f(x)=6(1-x^{2})-3(2x^{2})-2\f(x)=6-6x^{2}-6x^{2}-2\f(x)=-12x^{2}+4[/latex]   [latex]-12x^{2}+4=0/cdot(-1)\12x^{2}-4=0\[/latex]   [latex]4(3x^{2}-1)=0\4(sqrt{3} x-1)(sqrt{3} x+1)=0[/latex]   [latex]sqrt{3} x-1=0\sqrt{3} x=1\x_{1}=frac{1}{sqrt{3}} =frac{sqrt{3}}{3}[/latex]   [latex]sqrt{3} x+1=0\sqrt{3} x=-1\x_{2}=-frac{1}{sqrt{3}} =-frac{sqrt{3}}{3}[/latex] [latex]x_{1}, x_{2} - miejsca zerowe funkcji[/latex]

[latex]f(x)=6(1-x^2)-3(2x^2)-2 = 6 -6x^2 - 6x^2 - 2 = - 12x^2 + 4[/latex]   [latex]- 12x^2 + 4 = 0 / : (-4)[/latex] [latex]3x^2 - 1 = 0[/latex] [latex](sqrt{3}x)^2 - 1^2 = 0[/latex] [latex](sqrt{3}x - 1)(sqrt{3}x + 1) = 0[/latex] [latex]sqrt{3}x - 1 = 0 vee sqrt{3}x + 1= 0[/latex]   [latex]sqrt{3}x - 1 = 0 [/latex] [latex]sqrt{3}x = 1 / : sqrt{3} [/latex] [latex]x = frac{1}{sqrt{3}} = frac{sqrt{3}}{sqrt{3} cdot sqrt{3}} = frac{sqrt{3}}{3} [/latex] lub [latex]sqrt{3}x + 1 = 0 [/latex] [latex]sqrt{3}x = -1 / : sqrt{3} [/latex] [latex]x = -frac{1}{sqrt{3}} = -frac{sqrt{3}}{sqrt{3} cdot sqrt{3}} = -frac{sqrt{3}}{3} [/latex] Odp. Miejsca zerowe funkcji f to: [latex]x = frac{sqrt{3}}{3} i x = -frac{sqrt{3}}{3} [/latex]