Question

rozłóż wielomiany na czynniki i podaj ich pierwiastki

a) 3x²-12x

b) x³-3x²-x+3

c) x³+5x²-4x-20

d) 9x²-16

ex³-5x²+4x

Answer 1

a) 3x²-12x = 3x(x-4 )

x=0 ∨ x-4=0

x=0 ∨ x=-4

 

b) x³-3x²-x+3 = x²(x-3)-1(x-3) = (x²-1)(x-3)= (x-1)(x+1)(x-3)

x-1=0 ∨ x+1=0 ∨ x-3=0

x=1 ∨ x=-1 ∨ x=3

 

c) x³+5x²-4x-20 = x²(x+5)-4(x+5)= (x²-4)(x+5) = (x-2)(x+2)(x+5)

x-2=0 ∨ x+2=0 ∨ x+5=0

x=2 ∨ x=-2 ∨ x=-5

 

d) 9x²-16=0 | :9

x²=16/9 | √

x= -4/3 ∨ x= 4/3

 

e) x³-5x²+4x = x(x²-5x+4) = x(x-4)(x-1)

x²-5x+4=0 ∨ x=0

Δ=9

√Δ=3

x₁= 4    x₂=1