Prikazi cijelu temu
04.02.2011 14:56
04.02.2011 14:56
Predmet:Re: Zadaci iz algebre
f(x) = x2 + ax + c
g(x) = x2 + bx + d
f(x)*g(x) = x4+ax3+bx2+adx+bcx+cd=x4 + (a+b)x3 + (ab + c + d)x2 + (ad+bc)x + cd
[Iz uslova zadatka]= x4 + 8x3 + 23x2 + 28x + 12= x4+4x3+4x2+4x3+16x2+16x+3x2+12x+12= x2(x2+4x+4)+4x(x2+4x+4)+3(x2+4x+4)=
(x+1) (x+ 2)2(x + 3)
Imamo dva slucaja
1. f(x)*g(x) = (x2 + 4x + 3) (x2 + 4x + 4)
f(x)*g(x) = (x2 + 3x + 2) (x2 + 5x + 6)
1.1. f(x) = x2 + 4x + 3
g(x) = x2 + 4x + 4
(a,b,c,d) = (4,4,3,4)
1.2. f(x) = x2 + 4x + 4
g(x) = x2 + 4x + 3
(a,b,c,d) = (4,4,4,3)
2.1. f(x) = x2+3x + 2
g(x) = x2 + 5x + 6
(a,b,c,d) = (3,5,2,6)
2,2. f(x) = x2 + 5x + 6
g(x) = x2 + 3x + 2
(a,b,c,d) = (5,3,6,2)
Citat:
Posmatrajmo funkcije Zadatak 47
a + b=8
ab + c + d =23
ad + bc = 28
cd = 12
f(x) = x2 + ax + c
g(x) = x2 + bx + d
f(x)*g(x) = x4+ax3+bx2+adx+bcx+cd=x4 + (a+b)x3 + (ab + c + d)x2 + (ad+bc)x + cd
[Iz uslova zadatka]= x4 + 8x3 + 23x2 + 28x + 12= x4+4x3+4x2+4x3+16x2+16x+3x2+12x+12= x2(x2+4x+4)+4x(x2+4x+4)+3(x2+4x+4)=
(x+1) (x+ 2)2(x + 3)
Imamo dva slucaja
1. f(x)*g(x) = (x2 + 4x + 3) (x2 + 4x + 4)
f(x)*g(x) = (x2 + 3x + 2) (x2 + 5x + 6)
1.1. f(x) = x2 + 4x + 3
g(x) = x2 + 4x + 4
(a,b,c,d) = (4,4,3,4)
1.2. f(x) = x2 + 4x + 4
g(x) = x2 + 4x + 3
(a,b,c,d) = (4,4,4,3)
2.1. f(x) = x2+3x + 2
g(x) = x2 + 5x + 6
(a,b,c,d) = (3,5,2,6)
2,2. f(x) = x2 + 5x + 6
g(x) = x2 + 3x + 2
(a,b,c,d) = (5,3,6,2)
"Ne treba se stidjeti nikakvog posla, pa čak ni onog najprljavijeg; treba se stidjeti samo besposlenog života." - Tolstoj