Răspuns:
m∈{-1,9}
Explicație pas cu pas:
A(m;-m+2) ∈Gf ⇒f(m)=3m+2
f(m)=m²-5m-7
f(m)=3m+2 ⇒ m²-5m-7=3m+2
m²-5m-7-3m-2=0
m²-8m-9=0
avem ecuatie de gradul doi cu necunoscuta m
pasul 1 calculam Δ
Δ=(-8)²-4·1·(-9)=64+36=100
pasul 2 aflam m
m₁=(8-√100)/2=-2/2=-1
m₂=(8+√100)/2=18/2=9
Ecuatia de grad II: are forma : ax²+bx+c=0
Rezolvare: prin descompunerea in factori sau in suma de patrate .
Se calculeaza Δ=b²-4ac
a) daca Δ<0 ecuatia nu are solutii reale S=Ф
b) daca Δ=0 ecuatia are 2 solutii reale si egale.
[tex]\displaystyle x_{1} =x_{2} =-\frac{b}{2a}[/tex]
c) daca Δ>0 ecuatia are 2 solutii reale si distincte :
[tex]\displaystyle x_{1} =\frac{-b+\sqrt{delta} }{2a} \\\\ \\ x_{2} =\frac{-b-\sqrt{delta} }{2a}[/tex]
