Question

sa se compuna o ecuatie de gradul 2 carre are solutiile a)x1=-1, x2=2 b)x1= 3, x2=1 c)x1= -4, x2= -(1/2).cu detalii

Answer 1

Formarea ecuatiei de gradul 2 cand se cunosc radacinile : x²-Sx+P=0 , unde S - suma radacinilor si P - produsul radacinilor si x₁,x₂ - radacinile ecuatiei.
a)
x₁ = -1
x₂ = 2
S = x₁+x₂ = -1+2 = 1
P = x₁*x₂ = -1*2 = -2
Ecuatia : x²-x-2 = 0
b)
x₁ = 3
x₂ = 1
S = x₁+x₂ = 3+1 = 4
P = x₁*x₂ = 3*1 = 3
Ecuatia : x²-4x+3 = 0
c)
x₁ = -4
x₂ = $\frac{-1}{2}$
S = x₁+x₂ = -4- $\frac{-1}{2}$ = $\frac{-9}{2}$
P = x₁*x₂ = (-4)*($\frac{-1}{2}$) = 2
Ecuatia : x²+$\frac{-9}{2}$x+2 = 0