calcul mental, plus projet prog
[perso/Denise/lycee/2015-2016.git] / 1ere / calcul_mental / 2nddegre_erreurs.tex
1 \input{../../header_beamer.tex}
2
3 \begin{document}
4
5 \slide{Équations du second degré~: chercher l'erreur}
6
7 \slide{
8 1)
9 \[x^2 +x +1 = 0 \]
10 \[\Delta = 1^2 + 4\times 1 \times 1 = 5\]
11 Deux solutions~:
12 \[
13 x_1 = \frac{-1 + \sqrt{5}}{2} \qquad x_2 = \frac{-1 - \sqrt 5}{2}
14 \]
15
16 \cadrem{ \Sol = \{ \frac{-1+\sqrt 5}{2}; \frac{-1-\sqrt 5}{2} \} }
17 }
18
19 \slide{
20 2)
21 \[
22 x^2 - 2x + 1 = 0
23 \]
24 \[\Delta = -2^2 - 4 \times 1 \times 1 = -8 \]
25 Pas de solutions.
26
27 \cadrem{\Sol = \emptyset}
28 }
29
30 \slide{
31 3)
32 \[
33 x^2 -2x -8 = 0
34 \]
35 \[
36 \Delta = (-2)^2 -4\times(-8)\times 1 = 36
37 \]
38 Deux solutions~:
39 \[
40 x_1 = \frac{-2+\sqrt{36}}{2}= 2 \qquad x_2 = \frac{-2-\sqrt{36}}{2} = -4
41 \]
42 \cadrem{\Sol = \{-4; 2 \}}
43 }
44
45 \slide{
46 4)
47 \[
48 x^2 +4x + 4 = 0
49 \]
50 \[ \Delta = 4^2 -4\times 4 \times 1 = 0\]
51 Deux solutions~:
52 \[
53 x_1 = \frac{-4 + \sqrt{0}}{2} = -2 \qquad x_2 = \frac{-4 - \sqrt{0}}{2} = -2
54 \]
55
56 \cadrem{\Sol = \{-2; -2 \}}
57 }
58
59 \slide{
60 5) \[ x^2 + x = 1 \]
61 \[
62 \Delta = 1^2 - 4 \times 1 \times 1 = -3
63 \]
64 \cadrem{\Sol = \emptyset}
65 }
66 \end{document}