a) 4x²+4x+1=0
Pentru rezolvarea acestor ecuatii sunt necesare formulele pentru ecuatiile de gradul 2. Daca avem o ecuatie de tipul: ax²+bx+c=0, atunci trebuie calculat in primul rand delta, Δ=b²-4ac, dupa care exista trei cazuri:
1) Δ<0 => ecuatia nu are solutii reale
2) Δ=0 => ecuatia are o singura solutie, x=-[tex]\frac{b}{2a}[/tex]
3) Δ>0 => ecuatia are doua solutii, x1=[tex]\frac{-b+\sqrt{delta}}{2a}[/tex],x2=[tex]\frac{-b-\sqrt{delta}}{2a}[/tex]
Asadar pentru prima ecuatie avem: Δ=16=16=0 =>x=[tex]\frac{-4}{8}[/tex]=[tex]\frac{-1}{2}[/tex]
d)
-4x²+6x-5=0 <=> 4x²-6x+5=0
Δ=36-80=-44 <0 => ecuatia nu are solutii reale.
b) 5x²-7x+2=0
Δ=49-40=9 >0 => x1=[tex]\frac{7+3}{2}=\frac{10}{2}=5[/tex], x2=[tex]\frac{7-3}{2}=\frac{4}{2}=2[/tex]
e) 0,1x²-x-2,5=0 <=> [tex]\frac{1}{10}*x^{2} -x-\frac{25}{10}=0[/tex] |*10 <=> x²-10x-25=0
Δ=100+4*25=200 => [tex]x1=\frac{10+10\sqrt{2} }{2}=5+5\sqrt{2}[/tex], x2=[tex]\frac{10-10\sqrt{2}}{2}=5-5\sqrt{2}[/tex]
c) 3x²-2x+1=0
Δ=4-12=-8 <0 => ecuatia nu are solutii reale.
