[tex]zad.a\\\\2x^{2} -3=0\\\\(\sqrt{2} x)^{2} -(\sqrt{3} )^{2} =0\\korzystam~~ze~~wzoru~~skroconego~~mnozenia:~~x^{2} -y^{2} =(x-y)\cdot (x+y)\\\\(\sqrt{2} x-\sqrt{3} )\cdot (\sqrt{2} x+\sqrt{3} )=0\\\\\sqrt{2} x-\sqrt{3}=0~~\lor ~~\sqrt{2} x+\sqrt{3}=0\\\\x=\sqrt{\dfrac{3}{2} } ~~\lor~~x=-\sqrt{\dfrac{3}{2} } \\\\Odp:~~Rownanie~~posiada~~dwa~~rozwiazania.[/tex]
[tex]zad.b\\\\3x^{2} -2x+1=0\\\\a=3,~~b=-2,~~c=1\\\\\Delta =b^{2} -4ac\\\\\Delta = (-2)^{2} -4\cdot 3\cdot 1\\\\\Delta = 4-12\\\\\Delta = -8\\\\[/tex]
[tex]\Delta=-8~~\Rightarrow ~~\Delta <0 ~~\Rightarrow ~~funkcja~~kwadratowa~~nie~~ma~~miejsc~~zerowych\\\\Odp:~~Rownanie~~nie~~posiada~~rozwiazan.[/tex]
