Bonjour
Factoriser :
2x^2 + 3x
= 2x * x + 3 * x
= x(2x + 3)
3(x - 1) + (x - 1)(x + 2)
= (x - 1)(3 + x + 2)
= (x - 1)(x + 5)
Résolution de chaque inéquation :
2x^2 + 3x < 0
x(2x + 3) < 0
x = 0 ou 2x + 3 = 0
x = 0 ou 2x = -3
x = 0 ou x = -3/2
x.............|-inf........-3/2.......0........+inf
x.............|.......(-)...........(-)...o...(+)........
2x + 3....|.......(-)....o.....(+)......(+)........
Ineq......|........(+)....o.....(-)...o....(+)......
[tex]x \in ]-3/2 ; 0[[/tex]
3(x - 1) + (x - 1)(x + 2) > 0
(x + 1)(x + 5) > 0
x + 1 = 0 ou x + 5 = 0
x = -1 ou x = -5
x............|-inf.......-5......-1........+inf
x + 1......|.......(-)........(-)..o...(+)......
x + 5.....|.......(-)...o...(+).......(+)......
Ineq......|.......(+)..o...(-).o.....(+).....
[tex]x \in ]-\inf ; -5[ U ]-1 ; +\infty[[/tex]
