Question

Zadanie 7. Ile miejsc zerowych ma funkcja f?



b) f(x)= x²(x²-2)(x-2)²
------------------
(x-1)²(x+2)²

c) f(x)= x²(x²-9)(9x²+6x+1)
------------------------
x(x²+6x+9)

d) f(x)= (4x-1)²(1-4x)²(x²+4+4)
----------------------------
(x²+4)(x+4)²

Answer 1

b)  x₀ ≠ 1 i x₀ ≠ -2

 x₀ ∈ {-√2, 0, 2, √2}

4 msc zerowe.

 

c) x²+6x+9 = 0

Δ = 6² - 4*9*1 = 0

x = -6/2 = -3

 

x₀ ≠ 0 , x₀ ≠ -3

 

9x²+6x+1 = 0

Δ = 6² - 4*9*1 = 0

x = -6/ 18 = -⅓

 

x₀ ∈ {-⅓, 0, 3}

3 msc zerowe

 

d) x₀ ≠ 2, x₀ ≠ -2

4x -1 = 0

x = ¼

 

x²  + 4x + 4 = 0

Δ = 4² - 4*4*1 = 0

x = -4/2 = -2

 

x₀ ∈ {¼}

1 msc zerowe