[latex]a)\ \ 2x^2-9x-35=0\ \Delta = b^{2}-4ac = (-9)^{2}-4*2*(-35)=81+ 280=361\ \sqrt{Delta 5}=sqrt{361}=19\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{9-19}{4}=frac{-10}{4}=-frac{5}{2}=-2frac{1}{2}\ \x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{9+19}{4}=frac{28}{4}=7[/latex] [latex]b) \\x^2-13x+3=0\ \Delta = b^{2}-4ac = (-13)^{2}-4*1*3=169-12=157\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{13-sqrt{157}}{2}\ \x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{13+sqrt{157}}{2}[/latex] [latex]c)\-6x^2+13x+5=0\ \Delta = b^{2}-4ac = 13^{2}-4*(-6)*5=169+120=289\ \sqrt{Delta }=sqrt{289}=17\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{-13-17}{-12}=frac{-30}{-12}=frac{5}{2}\ \x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{-13+17}{-12}=frac{4}{-12}=-frac{1}{3}[/latex] [latex]d)\5x^2 -6x+6=0\ \Delta = b^{2}-4ac = (-6)^{2}-4*5*6=36-120=-84 \ \Delta <0[/latex] brak pierwiastków [latex]e)\-2x^2+5x-3=0\ \Delta = b^{2}-4ac = 5^{2}-4*(-2)*(-3)=25-24=1\ \sqrt{Delta }=sqrt{1}=1\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{-5-1}{-4}=frac{-6}{-4}=frac{3}{2}=1frac{1}{2}\ \x_{2}=frac{-b+sqrt{Delta }}{2a} = frac{-5+1}{-4}=frac{-4}{-4}=1[/latex] [latex]f)\\4x^2+12x+9=0\ \Delta = b^{2}-4ac = 12^{2}-4*4*9=1441-144=0\ \x_{0}=frac{-b}{2a} =frac{-12}{8}=-frac{3}{2}=-1frac{1}{2}[/latex]
Rozwiąż równanie. a) 11x +10=2x+37 b) 12x +6=9x + 12 c)10x +16=3x+2 d)13x +30=21x +14 Daje naj !...
