Équations algébriques

x x
ax +b= 0 2
3ax=b
cos (5x+ 1) = 3x2−2x x
anxn+. . . +a0= 0 ai
1 4
ax +b= 0
x=−b
a
a= 0
0
b= 0 x b 6= 0
ax2+bx+c= 0
a6= 0 1
a
a= 1
ax2+bx +c= 0
a0x2+b
ax+c a= 0
x2x21
x2
1
a= 1
x0=x+b
2b= 0

x2+c= 0
c < 0c= 0 c > 0
ax2+bx +c= 0
∆ = b2−4ac ∆
∆<0 ∆ = 0
−b
2a∆>0
−b−√∆
2a−b+√∆ 2a
½x+y=S
xy =P
S P
t t2−St +P= 0
ax3+bx2+cx +d= 0
a6= 0 2
a x0=x+b
3
a= 1 b= 0
x3+cx +d= 0
x p +q
p
q p +q x
p3+q3+ (p+q) (3pq +c) + d= 0
p q 3pq +c= 0
½3pq =−c
p3+q3=−d
d2
4+c3 27 >0x3+cx+d= 0

d2
4+c3 27 >0
f
f(x) = x3+cx +dd2
4+c3 27 = 0
−2q−c
3=−23
qd
2c
q−c
3=3
qd
2
c=d= 0 d2
4+c3 27 <0
f
x3−2x+1 = 0
1−1−√5
2−1+√5 2
ax4+bx3+cx2+dx+e= 0
a6= 0
a
a= 1 b= 0
x4+cx2+dx +e= 0
t
¡x2+t¢2−£(2t−c)x2−dx +¡t2−e¢¤= 0
2
t4 (2t−c) (t2−e) = d26= 0
(2t−c)x2−dx +¡t2−e¢= (2t−c)µx−d
4t−2c¶2
d6= 0 2t−c
d= 0 X=x2

5
anxn+. . . +a0= 0 n5
n
an6= 0 P(x) = anxn+. . . +a0
a P (a) = 0
n−1
a
a
1
k y
xk−yk= (x−y)¡xk−1+yxk−2+y2xk−1+... +yk−2x+yk−1¢
P(x)−P(y) (x−y)Qy(x)Qyn−1
x a P (x) = 0
P(x) = (x−a)Qa(x)
n n
Qa
P(x) = x5−5x3+8 x5−5x3+8 = 0
2
0
a2
1
²²
0−50 0 8
+2 4 −2−4−8
1
×2>>
2
×2
==
−1
×2;;
−2
×2;;
−4
×2;;
0

P(2)
P a
a
Qa
P(x) = (x−2) ¡x4+ 2x3−x2−2x−4¢
4
anxn+... +a0= 0
an6= 0 a06= 0
0x
ai
p
q
p q p a0q an
a bc a b
a c
p
qp a0q an
an= 1
a0an=a0= 1 1
anxn+. . . +
a0= 0 an=a06= 0 an−1=a1an−2=a2
x6−2x5+ 3x4−3x3+ 3x2−2x+ 1 = 0