Question

wyznacz pierwiastki wielomianu

f(x) = x^2- 2x- 48

^2 - kwadrat2

g(x) = 1/2 ( x+3 )(2x-1)+(3x-1) (2x-1)

wyznacz zbiór pierwiastków wielomianu .

f(x)= (x-3)(x +2)(x-13)

g(x)= (x-3 )(x^2+3x+9)

^2-kwadrat 2

Answer 1

1.

x^2-2x-48=0

Δ=4+192=196

x₁=(2-14)/2=-6

x₂=(2+14)/2=8

 

g(x)=1/2(x+3)(2x-1)+(3x-1)(2x-1)=(x+3)(x-0.5)+6x^2-5x+1=x^2+2.5x-1.5+6x^2-5x+1=7x^2-2.5x-0.5

 

7x^2-2.5x-0.5=0

Δ=6.25+14=20.25

x₁=(2.5-4.5)/14=-1/7

x₂=(2.5+4.5)/14=1/2

 

2.

f(x)=(x-3)(x+2)(x-13)

x₁=-2

x₂=3

x₃=13

 

g(x)=(x-3)(x^2+3x+9)

x^2+3x+9=0        - sprzeczność

x=3