Question

Równania wielomianowe:

a) (16-x²)(8x³+1)(x²+2x+6)=0

b)(x²+3x+2)(x²+1)(x²-2x-3)=0

c)(x²-x-6)(x²+4x+4)=0

d)(8x²-4x)(9x²+30x+25)=0

e) (9x²-16)(4x²+8)(x³-8)=0

Dziękuje ;)

Answer 1

a) (16-x²)(8x³+1)(x²+2x+6)=0

16-x²=0

-x²=16

x²=16

x=4  ∨  x= -4

 

8x³+1=0

8x³=-1

x³=-1/8

x=-½

 

x²+2x+6=0

Δ=2²-4*1*6=4-24= - 20 < 0

brak pierwiastków

 

b)(x²+3x+2)(x²+1)(x²-2x-3)=0

x²+3x+2=0

Δ=3²-4*1*2=9-8=1

√Δ=1

x₁=(-3+1)/2=-2/2=-1

x₂=(-3-1)/2=-4/2=-2

x²+1=0

x² ≠ -1

brak pierwiastków

 

x²-2x-3=0

Δ=(-2)²-4*1*(-3)=4+12=16

√Δ=4

x₁=(2+4)/2=6/2=3

x₂=(2-4)/2=-2/2=-1

 

c)(x²-x-6)(x²+4x+4)=0

x²-x-6=0

Δ=(-1)²-4*1*(-6)=1+24=25

√Δ=5

x₁=(1+5)/2=6/2=3

x₂=(1-5)/2=-4/2=-2

x²+4x+4=0

Δ=4²-4*1*4=16-16=0

x=-4/2=-2

d)(8x²-4x)(9x²+30x+25)=0

8x²-4x=0

4x(2x-1)=0

x=0  ∨  x=½

9x²+30x+25=0

Δ=30²-4*9*25=900-900=0

x=-30/18=-1⅔

e) (9x²-16)(4x²+8)(x³-8)=0

9x²-16=0

9x²=16

x²=16/9

x=4/3  ∨  x=-4/3

4x²+8=0

4x²=-8

x²=-2

brak pierwiastka

 

x³-8=0

x³=8

x=2 ∨ x=-2