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Apostila 4-Eq.2ºgrau Soma e Produto (1)
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Professor Elias Ferreira Santiago Apostila 4 4 Edio 2015
EQUAES DO 2 GRAU SOMA E PRODUTO DAS RAZES
EXERCCIOS:
1) Resolva as equaes do 2 grau atravs da soma e produto das razes:
a) x - 5x + 6 = 0
a = 1, b = -5, c = 6
S = -
= -
= 5 x = 2
V = ;
P =
=
= 6 x = 3
b) x - 7x + 10 = 0
c) x - 11x + 10 = 0
d) x - 11x + 18 = 0
e) x - 13x + 42 = 0
f) x - 9x + 20 = 0
g) x - 14x + 45 = 0
h) x - 12x + 35 = 0
i) x - 7x + 6 = 0
j) x - 8x + 12 = 0
k) x - 15x + 56 = 0
l) x - 13x + 40 = 0
m) x - 7x + 12 = 0
n) x - 8x + 7 = 0
o) x - 9x + 14 = 0
p) x - 12x + 20 = 0
q) x - 6x + 9 = 0
r) x - 10x + 25 = 0
s) x - 4x + 4 = 0
t) x - 2x + 1 = 0
u) x - 5x + 4 = 0
v) x - 4x + 5 = 0
2) Resolva as equaes do 2 grau atravs da soma e produto das razes:
a) 2x - 14x + 24= 0 : ( 2 )
x - 7x + 12=
a = 1, b = -7, c = 6 = 12
S = -
= -
= 7 x = 3
V = ;
P =
=
= 12 x = 4
b) 2x - 10x + 12= 0
c) 2x - 20x + 48= 0
Professor Elias Ferreira Santiago Apostila 4 4 Edio 2015
d) 3x - 18x + 24= 0
e) 4x - 32x + 60= 0
f) 5x - 50x + 105= 0
3) Resolva as equaes do 2 grau atravs da soma e produto das razes:
a) - x + 5x - 4 = 0 . (-1)
x - 5x + 4 = 0
a = 1, b = -5, c = 4
S = -
= -
= 5 x = 1
V = ;
P =
=
= 4 x = 4
b) - x + 11x - 24 = 0
c) - x + 12x - 20 = 0
d) - x + 12x - 36 = 0
e) - x + 10x - 21 = 0
f) - x + 5x - 4 = 0
4) Resolva as equaes do 2 grau atravs da soma e produto das razes:
a) - 2x + 20 x - 32 = 0 . (-1)
2x - 20x + 32 = 0 : ( 2 )
x - 10x + 16 = 0
a = 1, b = -10, c = 16
S = -
= -
= 10 x = 2
V = ;
P =
=
= 16 x = 8
b) - 2x + 22 x - 56 = 0
c) - 10x + 100 x - 90 = 0
d) - 4x + 52 x - 168 = 0
5) Resolva as equaes do 2 grau atravs da soma e produto das razes:
a) x - x - 6 = 0
a = 1, b = -1, c = -6
S = -
= -
= 1 x = - 2
V = ;
P =
=
= - 6 x = 3
Professor Elias Ferreira Santiago Apostila 4 4 Edio 2015
b) x + x - 6 = 0
a = 1, b = 1, c = -6
S = -
= -
= -1 x = 2
V = ;
P =
=
= - 6 x = - 3
c) x + 5x + 6 = 0
a = 1, b = 5, c = 6
S = -
= -
= -5 x = - 2
V = ;
P =
=
= - 6 x = - 3
d) x - 2x - 8 = 0
e) x + 2x - 8 = 0
f) x + 6x + 8 = 0
g) x - 2x - 15 = 0
h) x + 2x - 15 = 0
i) x + 8x + 15 = 0
j) x + 9x + 14 = 0
k) x - 4x - 21 = 0
l) x + 5x - 14 = 0
m) x + 15x + 54 = 0
n) x - 4x - 32 = 0
o) x + 7x - 18 = 0
p) 2x + 14x + 24 = 0
q) 4x - 12x - 40 = 0
r) - 2x + 8x + 24 = 0
s) 3x + 24x + 45 = 0
GABARITO 1) a) ; , b) ; , c) 1; 10 , d) ; , e) ; , f) 4; , g) 5; 9 , h) 5; 7 , i) 1; , j) ; , k) ; ,
l) ; , m) 3; 4 , n) 1,7 , o) 2; 7 , p) 2; 10 , q) 3 , r) 5 , s) , t) , t) ; , v) .
2) a) 3; 4 , b) 2; 3 , c) 4; 6 , d) 2; 4 , e) ; , f) ; .
3) a) 1; 4 , b) 3; 8 , c) 2; 10 , d) 6 , e) ; , f) ;
4) a) ; , b) ; , c) 1; 9 , d) ;
5) a) ; , b) ; , c) 3; 2 , d) ; , e) ; , f) ; , g) ; h) 3; 5 , i)
3; , j) ; , k) ; , l) ; , m) 6; 9 , n) 4,8 , o) 9; 2 , p) 3; 4 , q) 2, 5 , r) 2, 6 ; s) ; .