a) [latex]3x^2-4x-2=0\Delta =b^2-4ac = (-4)^2-4cdot 3cdot (-2)=16+24=40\sqrt{Delta }=sqrt{40}=sqrt{10cdot 4}=2sqrt{10}\x_{1}=frac{-b-sqrt{Delta }}{2a}=frac{4-2sqrt{10}}{2cdot 3}=frac{2(2-sqrt{10})}{6}=frac{2-sqrt{10}}{3}\x_{2}=frac{-b+sqrt{Delta }}{2a}=frac{4+2sqrt{10}}{2cdot 3}=frac{2(2+sqrt{10})}{6}=frac{2+sqrt{10}}{3}[/latex] b) [latex]4x^2+6x+frac{9}{4}=0 /cdot 4\16x^2+24z+9=0\Delta =b^2-4ac = 24^2-4cdot 16cdot 9=576 - 576=0[/latex]) gdy ∆ = 0 jest jeden pierwiastek [latex]x_{0}=frac{-b}{2a}=frac{-6}{2cdot 4}=frac{-6}{8}=-frac{3}{4}[/latex] c) [latex]x(x-5)=2x(x+1)\x^2-5x = 2x^2+2x \x^2-5x-2x^2-2x=0\-x^2-7x=0\ -x(x+7)=0\-x=0 vee x+7 = 0\x=0 vee x= -7[/latex] d) [latex]7x^2-3x+2<0\Delta =b^2-4ac = (-3)^2-4cdot 7cdot2= 9 - 56 = - 47[/latex] gdy ∆ < 0 nie ma pierwiastków e) [latex]5x^2> 8x-5\5x^2-8x+5>0\Delta =b^2-4ac = (-8)^2-4cdot 5cdot 5=64-100=-34[/latex] gdy ∆ < 0 nie ma pierwiastków f) [latex]-3x^2+2x-1<0\Delta =b^2-4ac = 2^2-4cdot (-3)cdot(-1)= 4 -12 = -12[/latex] gdy ∆ < 0 nie ma pierwiastków
