Question

am nevoie de 20de ecuati de gradul 2 rezolvatr

Answer 1

Ecuatia de gradul II are forma : ax² + bx + c = 0
Δ = b² -4ac
I · daca Δ > 0 , ecuatia are 2 solutii distincte : x₁ = (-b-√Δ) / (2a)
                                                                        x₂ = (-b+√Δ) / (2a)
II · daca Δ = 0 , ecuatia are o singura solutie : x = -b / (2a)
III ·daca Δ < 0 , ecuatia NU are solutii in IR

Iti dau ex. pt. fiecare :

1.

x² + 5x +6 = 0
Δ = 5² - 4*6*1
Δ = 25 -24
Δ = 1   > 0  → x₁ = (-5-√1) / (2*1)
                       x₁ = (-5-1) / 2
                       x₁ = -6/2
                       x₁ = -3

                  → x₂ = (-5+√1) / (2*1)
                       x₂ = (-5+1) / 2
                       x₂ = -4/2
                       x₂ = -2
⇒ x ∈ {-3,-2}

2.
x² + 6x + 9 = 0
Δ = 6² - 4*9*1
Δ = 36 - 36
Δ = 0   → x = -b/(2a)
                x = -6/2
                x = -3

3.
x² + 2x + 3 = 0
Δ = 2² - 4*3*1
Δ = 4 - 12
Δ = -8   < 0 → ecuatia nu are solutii in IR