Bartlett Lyons
10/21/2023 · Elementary School
oit le Polynome \( P(x)=-3 x^{3}+10 x-4 \) 1- Montrer que \( P(x) \) est factorisable par \( x+2 \). 2- Déterminer les réels a, bet c tels que \( P(x)=(x+2)\left(a x^{2}+b x+6\right. \) 3- Résoudre dans \( \mathbb{R} \), l'équation \( P(x)=0 \) 4- Etudier suivant les valeurs de \( x \), le signe de \( P(x) \). 5- En déduire le signe de \( P\left(\frac{\pi}{\sqrt{2}}\right) \) 6- Résoudre dans \( \mathbb{R} \), l'inéquation \( P(x) \leq 0 \) \( -3 x^{2}+6 x-2 \),
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1. \( P(x) \) is factorizable by \( x+2 \).
2. \( a = -3 \), \( b = 16 \), \( c = -36 \).
3. The solutions are \( x = -2 \), \( x = 2 \), and \( x = 6 \).
4. The sign of \( P(x) \) is positive for \( x \in (-\infty, -2) \) and \( x \in (2, 6) \), and negative for \( x \in (-2, 2) \) and \( x \in (6, +\infty) \).
5. The sign of \( P\left(\frac{\pi}{\sqrt{2}}\right) \) is positive.
6. The solutions to the inequality \( P(x) \leq 0 \) are \( x \in [-2, 2] \) and \( x \in [6, +\infty) \).
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