[tex]f(x)=-3x^{2} +4x-1~~\land~~D_{f(x)} =R\\zad.a\\\\f(-\sqrt{3} )=-3\cdot (-\sqrt{3} )^{2} +4\cdot (-\sqrt{3} )-1\\\\f(-\sqrt{3} )=-3\cdot 3-4\sqrt{3} -1\\\\f(-\sqrt{3} )=-9-4\sqrt{3} -1\\\\f(-\sqrt{3} )=-10-4\sqrt{3} \\\\zad.b\\\\f(x)=-3x^{2} +4x-1~~\land ~~f(x)=0~~\Rightarrow~~-3x^{2} +4x-1=0\\\\-3x^{2} +4x-1=0\\a=-3,~~b=4,~~c=-1\\\Delta = b^{2} -4ac\\\Delta = 4^{2} -4\cdot (-3)\cdot (-1)\\\Delta = 16-12\\\Delta=4,~~\sqrt{\Delta} =2\\\\[/tex]
[tex]x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a} \\\\x_{1} =\dfrac{-4-2}{-6} ~~\lor~~x_{2} =\dfrac{-4+2}{-6}\\\\x_{1} =\dfrac{-6}{-6} ~~\lor~~x_{2} =\dfrac{-2}{-6}\\\\x_{1} =1~~\lor~~x_{2} =\dfrac{1}{3}[/tex]
