Question

Relatia X₁+X₂= -b/a,este valabila pentru ecuatia,ax²+bx+c=0,a≠0,cu solutiile reale X₁ si X₂.
Calculati X₂ pentru ecuatia :

a) 7X²-19X+12=0,daca X₁=1.
b) -X²+14X-24=0,daca X₁=2.
c) 1/3X²-5/12X-3/4=0,daca X₁= -1.
d) 5X²+√3X-12=0,daca X₁= -√3.
Vreau rezolvarea completa va rog !

Answer 1

a) 7X²-19X+12=0,daca X₁=1.
x₁+x₂=19/7
1+x₂=19/7
x₂=19/7-1=12/7

b) -X²+14X-24=0,daca X₁=2.
x₁+x₂=(-14)/(-1)=14
2+x₂=14
x₂=14-2=12

c) 1/3X²-5/12X-3/4=0,daca X₁= -1
x₁+x₂=(5/12)/(1/3)=5/4
-1+x₂=5/4
x₂=5/4+1=9/4

d) 5X²+√3X-12=0,daca X₁= -√3.
x₁+x₂=-√3/5
-√3+x₂=-√3/5
x₂=-√3/5+√3 =4√3/5