Question

1) rozwiąż równania wielomianowe:
a) x³-3x²-4x+12=0
b) x³-7x²+12x=0
2) rozłóż wielomiany na czynniki:
a) W(x)=x³-4x²-5x+20
b) W(x)=x³-5x²-3x+15
c) W(x)=5x³-6x²+x

Answer 1

A) x³-3x²-4x+12=0
x²(x-3)-4(x-3)=0
(x²-4)(x-3)=0
(x+2)(x-2)(x-3)=0
x+2=0 ∨ x-2=0 ∨ x-3=0
x=-2 ∨ x=2 ∨ x=3
x={-2,2,3}

b) x³-7x²+12x=0
x(x²-7x+12)=0
x(x-3)(x-4)=0
x=0 ∨ x-3=0 ∨ x-4=0
x=0 ∨ x=3 ∨ x=4
x={0,3,4}

a) W(x)=x³-4x²-5x+20=x²(x-4)-5(x-4)=(x²-5)(x-4)=(x+√5)(x-√5)(x-4)
b) W(x)=x³-5x²-3x+15=x²(x-5)-3(x-5)=(x²-3)(x-5)=(x+√3)(x-√3)(x-5)
c) W(x)=5x³-6x²+x=x(5x²-6x+1)=x(5x-1)(x-1)