5. b) [latex]x^2+x-frac{3}{4}=0[/latex] [latex]a=1[/latex] [latex]b=1[/latex] [latex]c=-frac{3}{4}[/latex] [latex]Delta=b^2-4ac=1^2-4 cdot 1 cdot left(-frac{3}{4} ight)=1+3=4[/latex] [latex]sqrt{Delta}= sqrt{4}=2[/latex] [latex]x_1= frac{-b-sqrt{Delta}}{2a}= frac{-1-2}{2}= frac{-3}{2}=-1 frac{1}{2}[/latex] [latex]x_2= frac{-b+sqrt{Delta}}{2a}= frac{-1+2}{2}= frac{1}{2}[/latex] d) [latex]x^2+5x-6=0[/latex] [latex]a=1[/latex] [latex]b=5[/latex] [latex]c=-6[/latex] [latex]Delta=b^2-4ac=5^2-4 cdot 1 cdot (-6)=25+24=49[/latex] [latex]sqrt{Delta}= sqrt{49} =7[/latex] [latex]x_1= frac{-b-sqrt{Delta}}{2a}= frac{-5-7}{2}= frac{-12}{2}=-6[/latex] [latex]x_2= frac{-b+sqrt{Delta}}{2a}= frac{-5+7}{2}= frac{2}{2}=1[/latex] h) [latex]x^2-7x-8=0[/latex] [latex]a=1[/latex] [latex]b=-7[/latex] [latex]c=-8[/latex] [latex]Delta=b^2-4ac=(-7)^2-4 cdot 1 cdot (-8)=49+32=81[/latex] [latex]sqrt{Delta}= sqrt{81} =9[/latex] [latex]x_1= frac{-b-sqrt{Delta}}{2a}= frac{7-9}{2}= frac{-2}{2}=1[/latex] [latex]x_2= frac{-b+sqrt{Delta}}{2a}= frac{7+9}{2}= frac{16}{2}=8[/latex] ================ 6. f) [latex]x^2-x-frac{1}{4}=0[/latex] [latex]a=1[/latex] [latex]b=-1[/latex] [latex]c=-frac{1}{4}[/latex] [latex]Delta=b^2-4ac=(-1)^2-4 cdot 1 cdot left(-frac{1}{4} ight)=1+1=2[/latex] [latex] sqrt{Delta}= sqrt{2} [/latex] [latex]x_1= frac{-b-sqrt{Delta}}{2a}= frac{1- sqrt{2} }{2}[/latex] [latex]x_2= frac{-b+sqrt{Delta}}{2a}= frac{1+sqrt{2} }{2}[/latex]
