Réponse :
Explications étape par étape
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(x - 5)(-2x^2 + 15x - 7) >> 0
x - 5 = 0 ou -2x^2 + 15x - 7 = 0
x = 5 ou [tex]\Delta = 15^{2} - 4 * (-2) * (-7) = 225 - 56 = 169 = 13^{2}[/tex]
x = 5 ou [tex]\sqrt\Delta = 13[/tex]
x1 = (-15 - 13)/(2 * (-2)) = -28/-4 = 7
X2 = (-15 + 13)/(-4) = -2/-4 = 1/2
x........|-inf......1/2......5.......7.......+inf
x-5....|.......(-).......(-)...o...(+)....(+).......
Poly..|.......(-)...o.(+).......(+).o...(-).......
Ineq.|........(+)..o..(-)..o...(+).o...(-)......
[tex]x \in ]-\infty ; 1/2] U [5 ; 7][/tex]
(2x - 3)/(x^2 + 6x + 9) < 0
(2x - 3) / (x + 3)^2 < 0
2x - 3 = 0
2x = 3
x = 3/2
x + 3 # 0
x # -3
x.............|-inf.......-3......3/2........+inf
2x-3 ......|......(-)........(-)....o...(+).......
(x+3)^2..|......(+)...o..(+).........(+)......
Ineq.......|......(-)....||...(-)....o....(+)......
[tex]x \in ]-\infty ; -3[ U ]-3 ; 3/2[[/tex]
x^2 + 7x + 12 >> 0
[tex]\Delta = 7^{2} - 4 * 1 * 12 = 49 - 48 = 1[/tex]
X1 = (-7 - 1)/2 = -8/2 = -4
X2 = (-7 + 1)/2 = -6/2 = -3
x........|-inf.....-4........-3........+inf
Ineq.|.....(+)...o...(-)...o...(+).......
[tex]x \in ]-\infty ; -4] U [-3 ; +\infty[[/tex]
