Matemática - Funciones

Contenido

Ejercicios de Funciones: Función Cuadrática.

1) Resolver las siguientes ecuaciones fraccionarias de segundo grado:

a- (x + 2)/(x - 3) = (3.x - 4)/(x + 2)

b- (2.x - 2)/(x - 3) = (x + 2)/(x - 4)

c- (x + 1)/(x + 3) + (x - 3)/(x - 1) = 5/4

d- (x + 1)/(x + 2) ² + 3.x/(x + 2) = 1/4

e- [(x + 1)/(x - 1)] ² + (x + 1)/(x - 1) - 6 = 0

f- 5/(x + 1) ² + 4/(x - 1) = 1

g- (x ² - 1)/(x - 2) + 5 = 3/(x - 2)

h- 3/(x - 2) + 2/(x - 3) = 2/(x - 4)

i- x/6 + 6/x = 6

j- 6/(x - 1) + 2/(x - 2) = 3/(x - 3)

k- 4/(x + 4) + 1/(x + 3) + 3/(x + 1) = 0

l- 6/(x + 2) - 3/(x ² - x - 6) = 20/(9 - x ²)

m- 4/(x ² - x - 2) + 2/(x + 1) = 7,5/(x ² - 4)

n- (x ² + x + 3)/(x ² - x + 3) = (2.x + 5)/(2.x + 7)

o- 3.x/(2.x + 1) = (x + 5)/(x + 1) + (x - 19)/(2.x ² + 3.x + 1)

p- (5.x - 2)/(2.x + 2) + (3.x + 2)/(4.x - 4) = 5.x/(x ² - 1) + 15/7

2) Resolver:

3) Determinar k de modo que cada ecuación tenga sus raíces iguales:

a) x ² - 5.x + k = 0

b) 3.x ² + 8.x + k = 0

c) 2.x ² - 6.x + k = 0

d) 25.x ² + k.x + 1 = 0

e) k.x ² + k.x + 1 = 0

f) k.x ² - 3.x + k = 0