[tex]Fie\ o\ ecuatie\ de\ grad\ 2\ cu\ radacinile\ x_1\ si\ x_2. \\ Ecuatia\ are\ forma \\ x^2-Sx+P=0 \\ unde\ S=x_1+x_2 \\ P=x_1x_2[/tex]
a)
[tex]S=3-4=-1 \\ P=-12 \\ ecuatia:\ x^2+x-12[/tex]
b)
[tex]S=-10-10=-20 \\ P=100 \\ ecuatia:\ x^2+20x+100[/tex]
c)
[tex]S=0 \\ P=0 \\ ecuatia:\ x^2=0[/tex]
d)
[tex]Alegem\ x_1=1\ x_2=3 \\ S=4 \\ P=3 \\ ecuatia:\ x^2-4x+3=0[/tex]
e)
[tex]luam\ x_1=-1\ x_2=-4 \\ S=-5 \\ P=4 \\ ecuatia:\ x^2+5x+4=0[/tex]
f) Ne trebuie un discriminant negativ, adica
[tex]b^2-4ac\ \textless \ 0 \\ 4ac\ \textgreater \ b^2 \\ Putem\ lua\ b=0\ si\ a=1\ c=2 \\ avem\ x^2+2=0 \\ Nu\ are\ solutii\ reale.[/tex]
