Question

Wyznacz miejsca zerowe funkcji f okreslonej podanym wzorem.

a)f(x)=4x-1/2

b)f(x)=(2x+4)(3x-5)

c)f(x)=x kwadrat - 25

d)f(x)=(1-x kwadrat)(4x kwadrat - 9)

POMOCYY DAMM NAJJJ PLISKAAAA;)(

Answer 1

a)

f(x) = 4x - 1/2

4x - 1/2 = 0

4x = 1/2

x = 1/8 

 

M.Z.: x = 1/8 

 

b)

f(x) =(2x+4)(3x-5)

(2x+4)(3x-5) = 0

6x^2 -10x +12x - 20 = 0

6x^2 + 2x - 20 = 0

2(3x^2 + x -10) = 0

D(delta) = 1 +120 = 121

VD = V121 = 11

x1 =(-1-11)/6 = -2

x2 =(-1+11)/6 = 5/3 = 1 2/3

 

M.Z.: x = -2   u    x = 1 2/3  

 

c)

f(x) = x^2 - 25

x^2 -25 = 0

(x+5)(x-5) = 0

x1 = -5

x2 = 5

 

M.Z.: x = -5,   u   x = 5

 

d)

f(x) =(1-x^2)(4x^2 - 9)

(1-x^2)(4x^2 - 9) = 0

(x+1)(x-1)(2x+3)(2x-3) = 0

x1 = -1

x2 = 1

2x+3 = 0

2x = -3

x3 = -3/2 = -1,5

2x-3 = 0

2x = 3

x4 = 3/2 = 1,5

 

M.Z.: x = -1,5,  u  x = -1,   u   x = 1,   u   x = 1,5