a=m
b=6(m+1)
c=9m+31
Δ= [6(m+1)]²-4·m·(9m+31)
Δ=36(m+1)²-4m(9m+31)
Δ=36(m²+2m+1)-36m²-124m
Δ=36m²+72m+36-36m²-124m
Δ=-52m+36.
Δ=0. -52m+36=0⇒-52m=-36⇒m=[tex] \frac{36}{52} [/tex]=[tex] \frac{9}{13} [/tex]
faci tabel pentru Δ
m| -inf [tex] \frac{9}{13} [/tex] +inf
Δ |+++++++++0-------------------------
s=[tex] \frac{-b}{a} [/tex]= -[tex] \frac{6(m+1)}{m} [/tex]= -[tex] \frac{6m+6}{m} [/tex]
egalezi cu 0 si faci tabel
-6m-6=0⇒m=-1
m=0
m | -inf -1 0 +inf
-6m-6|++++++++++0------------------------------
m |-------------------------------0+++++++++++++
fractia|-----------------0+++++++/-----------------------
p=[tex] \frac{c}{a} [/tex]=[tex] \frac{9m+31}{m} [/tex]
9m+31=0⇒m=-[tex] \frac{31}{9} [/tex]
m=0
m | -inf -[tex] \frac{31}{9} [/tex] 0 +inf
9m+31|------------------0+++++++++++++++++++++++++++++
m |-----------------------------------------------------0+++++++++
fractia |+++++++++++0---------------------------------/++++++++++
faci axa nr reale si pui toate valorile obtinute la m.
apoi faci alt tabel si te uiti pe fiecare interval ce semne au delta,p si s
m Δ p s Discutie
m∈(-inf;-31/9) Δ: + p: + s:- Discutie: x1 si x2∈R,x1<0,x2<0
m∈(-31/9; -1) Δ: + p:- s: - Discutie: x1,x2∈R,x1>0,x2<0, |x1|<|x2|
m∈(-1;0) Δ:+ p:- s:+ Discutie x1,x2∈R,x1>0,x2<0 si |x1|>|x2|
m∈(0; 9/13) Δ:+ p:+ s:- Discutie x1,x2∈R,x1<0,x2<0
m∈(9/13; +inf) Δ:- p:+ s:- Discutie x1,x2∉R
Analiza capete:
m=-31/9⇒-31/9x²+6(-31/9+1)x+9·(-31/9)+31=0 si calculezi normal
m=-1⇒-x²+6(-1+1)x+9(-1)+31=0 si calculezi normal
m=0⇒0+6(0+1)x+0+31=0 la fel,calculezi normal
m=9/13⇒9/13x²+6(9/13+1)+9·9/13+31=0 idem
