a) [tex] x^{2} -4x+3=0[/tex]
Δ=[tex]b^{2}-4ac=(- 4)^{2}-4*1*3=16-12=4[/tex]
[tex] x_{1} = \frac{-b+ \sqrt{delta} }{2a} = \frac{-(-4)+ \sqrt{4} }{2*1} = \frac{4+2}{2} =\frac{6}{2}=3[/tex]
[tex] x_{2} = \frac{-b- \sqrt{delta} }{2a} = \frac{-(-4)- \sqrt{4} }{2*1} = \frac{4-2}{2} =\frac{2}{2}=1[/tex]
x∈{1; 3}
b) [tex] x^{2} +x-2=0[/tex]
Δ=[tex]b^{2}-4ac=1^{2}-4*1*(-2)=1-(-8)=1+8=9[/tex]
[tex] x_{1} = \frac{-b+ \sqrt{delta} }{2a} = \frac{-(-1+ \sqrt{9} }{2*1} = \frac{-1+3}{2} =\frac{2}{2}=1[/tex]
[tex] x_{2} = \frac{-b- \sqrt{delta} }{2a} = \frac{-1- \sqrt{9} }{2*1} = \frac{-1-3}{2} =\frac{-4}{2}=-2[/tex]
x∈{-2;1}
