Correction

1 2 ◦2
a) 3x2−3x+3
4= 0
∆=(−3)2−4×3×3
4= 0
x=−b
2a=1 2S=1 2
b)1
2−4x2−x= 0
c)−5x2−2x+ 3 ≤0
∆ = (−2)2−4×(−5) ×3 = 64 = 82
x1=2−8
−10 =3 5x2=2+8 −10 =−1
a=−5
S=] − ∞;−1] ∪[3
5; +∞[.
d) (x+ 10) (−3x2+ 5x−4) >0
(E)x4−6x2+ 8 = 0.
t=x2(E)
(E0)t2−6t+ 8 = 0
t2−6t+ 8 = (x2)2−6x2+ 8 = x4−6x2+ 8
∆=(−6)2−4×8=4=22(E0)
t1= 2 t2= 4 t=x2
x2= 2 x2= 4,
−2−√2√2 2
S=n−2; −√2; √2; 2o
0,5
L l L =3
2l l L
q
C(q) = 0,2q2−6q+ 50.
a) 20

q20
C(20) = 0,2×202−6×20 + 50 = 10
20
b) 250
q C(q) = 250
0,2q2−6q+ 50 = 250 ⇐⇒ 0,2q2−6q−200 = 0
−20 50
50
6
a)V(q)q q
V(q)=6q
b)V(20) V(60)
V(20) = 120 V(60) = 360
V(q)< C(q)⇐⇒ V(q)−C(q)<0⇐⇒ −0,2q2+ 6q−50 <0
∆ = 104
q1= 30 −5√26 '4,5q2= 30 + 5√25 '54,5
a
a, b, c P (x) = ax2+bx +c
P(0) = 2, P (1) = 3, P (3) = −1.
P(0) = c= 2 c= 2
P(1) = a+b+c=a+b+ 2 = 3 a+b= 1
P(3) = 9a+3b+c= 9a+3b+2 = −1 9a+3b=−3 3a+b=−1
c= 2
a+b= 1
3a+b=−1
c= 2
a=−1
b= 2
P(x) = −x2+ 2x+ 2