1. [tex]x^{2} -3x+2=0\\[/tex]
Identificăm coeficienții: a=1 b=-3 c=2;
Calculăm Δ
Δ[tex]={b^{2} -4*ac}[/tex]
Δ=[tex]{(-3)^{2} -4 *1*2}=9-8=1[/tex]
Aflăm [tex]x_{1} , x_{2}.[/tex]
[tex]x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{3+1}{2*1} =\frac{4}{2} =2\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{3-1}{2*1} =\frac{-2}{2} =1[/tex]
S={1;2}
2. [tex]x^{2} -5x+6=0\\[/tex]
Identificăm coeficienții: a=1 b=-5, c=6;
Calculăm Δ
Δ=[tex]={b^{2} -4*ac}[/tex]
Δ=[tex]{(-5)^{2} -4 *1*6}=25-24=1[/tex]
[tex]x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{5+1}{2*1} =\frac{6}{2} =3\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{5-1}{2*1} =\frac{4}{2} =2\\[/tex]
S={2;3}
3. [tex]x^{2} -9x+20=0\\[/tex]
Identificăm coeficienții: a=1 b=-9, c=20;
Calculăm Δ
Δ[tex]={b^{2} -4*ac}[/tex]
Δ=[tex]{(-9)^{2} -4 *1*20}=81-80=1[/tex]
[tex]x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{9+1}{2*1} =\frac{10}{2} =5\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{9-1}{2*1} =\frac{8}{2} =4\\[/tex]
S={4;5}
4. [tex]x^{2} +5x+6=0\\[/tex]
Identificăm coeficienții: a=1 b=5, c=6;
Calculăm Δ
Δ[tex]={b^{2} -4*ac}[/tex]
Δ[tex]={(5)^{2} -4 *1*6}=25-24=1[/tex]
[tex]x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{-5+1}{2*1} =\frac{-4}{2} =-2\\\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{-5-1}{2*1} =\frac{-6}{2} =-3\\[/tex]
S={-3;-2}
