Question

Va rog frumos ajutati-ma, dau coroana!;)
Alcatuiti o ecuatie de gradul 2 care are multimea solutiilor: S={ -2;6 } , S={ -3;-1 }

Answer 1

Răspuns:

Explicație pas cu pas:

a) S₁ ={ -2;6 } ,

b) S₂ = { -3;-1 }

Ecuatia de gradul 2 = ax²+bx+c = 0

a) S₁ ={ -2;6 } <=> x₁ = -2  ; x₂ = 6

Ecuatia devine :  (x+2)(x-6) = 0  <=> x²-6x+2x-12 =0  <=>

x²-4x-12 = 0

Ecuatia generala = a(x²-4x-12) = 0

b) S₂ = { -3;-1 }  <=> x₁ = -3  ; x₂ = -1

Ecuatia devine :  (x+3)(x+1)  = 0 <=> x²+x+3x+3 = 0 <=>

x²+4x+3 = 0

Ecuatia generala = a(x²+4x+3) = 0