Semana 2algebra
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Transcript of Semana 2algebra
BIOLOGA
UNMSM
Algebra
SEMANA 2POLINOMIOS V.N. - GRADOS1. Sea el polinomio:P(X) = (xn(1 + 2xn(2 + n)n, si 2n veces su trmino independiente es igual a la suma de sus coeficientes, entonces n es:A)1
B) 2
C) 3D)4
E) 5
RESOLUCINT.I. = P(o) = nn
= P(1) = (1 + 2 + n)n( 2n . nn = (3 + n)n( 2n = 3 + n ( n = 3RPTA.: C2. Calcule m si la expresin:
se transforma a una expresin algebraica racional entera de 5to grado.A)8
B) 9
C) 10D)11
E) 12
RESOLUCIN
(
( m = 9
RPTA.: B3. Calcule n para que el monomio sea de 2 grado.
A)4
B) 5
C) 6D)8
E) 9
RESOLUCIN
(M(x) = x6n ( 22 = x2 ( 6n ( 22 = 2
( n = 4RPTA.: A4. Si:
Halle el grado absoluto de:
transformable a una E.A.R.E.A)3
B) 4
C) 5D)7
E) 8
RESOLUCINEl G.A. =
de la condicin:
Propiedad de proporciones:
(
Lo reemplazamos en (
RPTA.: C5. Si: P(x+5) = x ( 3x + 1Calcule: E = P(8) + P(6)A)0
B) 1
C) 2D)3
E) 7
RESOLUCINE = 3 ( 3(3) + 1 + 1 ( 3 + 1
E = 0RPTA.: A6. Del siguiente polinomioP(x; y) = 7xa+3yb(2z6(a+5xa+2yb(3za+ben donde:
G.Rx ( G.Ry = 3 ( G.A(P) = 13Calcule: a + b
A)6
B) 7
C) 8D)11
E) 12
RESOLUCING. RX = a + 3G.A(P) = a+b+1
G. Ry = b ( 2
( a + b = 12RPTA.: E7. Sea P(x) un polinomio lineal tal que verifica la relacin
Para todo valor de x. Halle P(4)A)17
B) 18
C) 19D)32
E) 33
RESOLUCINSea P(x) = ax + b ( P(6X) = 6ax + b(P(P(x)) = a(ax+b)+b = ax+ab+b
Luego:
ax + ab + b ( 6ax ( b = (9x+21
((a ( 6a)x + ab = (9x + 21
(a ( 6a = (9 ( ab = 21
(a(3) = 0
(a = 3
(3b = 21
b = 7
Entonces: P(x) = 3x + 7
( P(4) = 3(4) + 7 = 19
RPTA.: C8. Calcule n, si el G.A. del monomio es 6.
A)12
B) 13
C) 14D)11
E) 10
RESOLUCING.A. =
(30n ( 60 + 40n + 60 ( 24n ( 192 = 360
46n = 360 + 192
46n = 552
( n = 12
RPTA.: A9. Calcule n si el monomio es de 4to. grado
A)1
B) 3
C) 2
D)
E)
RESOLUCIN
(
3n + 6 + 1 = 24n
(7 = 21n
( n =
RPTA.: E10. Si:
Adems P(P(x)) es independiente de x. Calcule n
A)(1
B) 8
C)
D)(8
E) 5
RESOLUCIN
como es independiente de x se cumple:
65n + 65 =
n ( 16n + 64
64n + 16n + 1 = 0
8n
1 ( n = (
8n
1RPTA.: C11. Si:
Calcule: P((1)A)(1
B) 4
C) (4
D)5
E) 1
RESOLUCINComo es lineal, entonces: P(x) es lineal. Luego P(x) = ax + b
(P(P(P(x))) = ax + ab + ab + b
27x + 52 = a + ab + ab + b
(a = 3
(b = 4
( P(x) = 3x + 4
P((1) = (3 + 4 = 1
RPTA.: E12. Halle la suma de los valores de n que hacen que la expresin:
sea racional entera.A)7
B) 8
C) 9D)12
E) 13
RESOLUCINn ( 3 ( 0 (
n ( 3 ( n = 3( n ( 7
n = 6
(n = 3 (n = 6
RPTA.: C13. Sabiendo que:
son semejantes. Calcule el menor valor de m + n.A)1
B) 3
C) 5D)8
E) 13
RESOLUCINSi: P(x; y) ( Q(x; y)
(m ( 2 = n + 5 ( m ( n = 7 ....(()
(n + 5 = m+4 ( n(m = (1 ...(()
( + (: n ( n ( 6= 0
( n = 3 ( n = (2Luego:
n = 3
( m = 10
n = (2( m = 5
( menos: m + n = 3RPTA.: B14. Sea P(x) = x + 3x + 3x + 1Calcule: P(P((1)) + P(P(1))A)0
B) (3
C) 728D)729E) 730
RESOLUCINP(x)= (x+1) ( P((1)=0 ( P(P((1)) = 1
P(1) = (2) =8 (
P(P(1)) = P(8) = 9 = 729
( P(P((1)) + P(P(1)) = 1+729 = 730RPTA.: E15. Si el polinomio en x e yP(x, y) = 5xa + 3xbyc + 2xcyb + ya es homogneo ordenado y completo respecto de x e y.
Calcule: 2a + b + 3cA)17
B) 13
C) 15D)16
E) 18
RESOLUCINPor ser ordenado y completo:
a = 3; b = 2 y c = 1( 2(3) + 2 + 3(1) = 6 + 2 + 9 = 17RPTA.: A16. Calcule m si el polinomio
es completo y ordenado; en forma ascendente; de 4nn trminos.A)4
B) 5
C) 6D)7
E) 8
RESOLUCINEs ordenado en forma ascendente:
(n2n ( 8n = 0( n = 2Luego:
El nmero de trminos es:
m ( m + 3 + 1(m ( m + 4 = 4nnm ( m + 4 = 16
( m ( m ( 12 = 0( m = 4RPTA.: A17. Halle a y b en la identidad:
A)1 y 3
B)
C)
D) 1 y
E)0 y 1RESOLUCINaa = bb (
a ( ab = b4a ( b = 2a
( a =
RPTA.: C18. Siendo: P(xn + 1) = x ( 1Halle: n, si: P(3) =
A)
B)
C)
D)
E)
RESOLUCIN
xn + 1 = 3 ( xn = 2 ( x =
Luego:
P(3) =
(
RPTA.: E19. Sea P(x) un polinomio
P(x) = (3x ( 1)n+5x + 1; adems la suma de coeficientes es 70. Calcule el valor de:
A)6
B) 5
C) 4D)12
E) 3
RESOLUCIN
( 2n = 64 ( n = 6
RPTA.: C20. Dado el polinomio mnicoP(x) = 5x4 ( 7ax5 + (n(2)x7(4x ( 1
Calcule el valor de: nnA)1
B) 4
C) 27D)25
E) 16
RESOLUCINPor ser mnico y de una variable x (coeficiente principal = 1)((n ( 2) = 1 ( n = 3
Luego nos piden: nn = 33 = 27
RPTA.: C(
SAN MARCOS 2013 CUESTIONARIO DESARROLLADO
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