Réponses

2014-02-06T00:16:16+01:00
Bonsoir,

1) (x - 1) (x + 1) (x-2) < 0
Racines : x - 1 = 0 ==> x = 1
              x + 1 = 0 ==> x = -1
              x - 2 = 0 ===> x = 2

\begin{array}{|c|ccccccccc||}x&-\infty&&-1&&1&&2&&+\infty\\ x-1&&-&-&-&0&+&+&+&\\ x+1&&-&0&+&+&+&+&+&\\ x-2&&-&-&-&-&-&0&+&\\ Produit&&-&0&+&0&-&0&+ \\\end{array}\\\\\\S=]-\infty:-1[\ \cup\ ]1;2[

2) x(2x + 1) (3x - 4) (x + 2) ≥ 0
Racines : x = 0
              2x + 1 = 0 ==> 2x = -1  ===> x = -1/2
              3x - 4 = 0 ==> 3x = 4  ===> x = 4/3
              x + 2 = 0 ===> x = -2
 
\begin{array}{|c|ccccccccccc||}x&-\infty&&-2&&-\dfrac{1}{2}&&0&&\dfrac{4}{3}&&+\infty\\ x&&-&-&-&-&-&0&+&+&+&\\ 2x+1&&-&-&-&0&+&+&+&+&+&\\ 3x-4&&-&-&-&-&-&-&-&0&+&\\x+2&&-&0&+&+&+&+&+&+&+\\Produit&&+&0&-&0&+&0&-&0&+\\\end{array}\\\\\\S=]-\infty:-2]\ \cup\ [-\dfrac{1}{2};0]\ \cup\ [\dfrac{4}{3};+\infty[