zad 1 a) W(x)=-3x²+4x W(x)=-3x(x - 4/3) ---------------------------- b) W(x)=x³–x²+9x-9 W(x)=x²(x-1)+9(x-1) W(x)=(x²+9)(x-1) ---------------------------- c) W(x)=4x²+20x+25 W(x)=4(x² + 5x + 25/4) W(x)=4(x + 5/2)² ===================== zad 2 a) x³+4x²–2x–8=0 x²(x+4)-2(x+4)=0 (x²-2)(x+4)=0 (x-√2)(x+√2)(x+4)=0 x=√2 lub x=-√2 lub x=-4 ---------------------------- b) 3x⁴ –10x³+10x–3 = 0 3x⁴-3-10x³+10x=0 3(x⁴-1)-10x(x²-1)=0 3(x²-1)(x²+1)-10x(x²-1)=0 (x²-1)[3(x²+1)-10x]=0 (x-1)(x+1)[3x²-10x+3]=0 x-1=0 lub x+1=0 lub 3x²-10x+3=0 x=1 x=-1 x=1/3 x=3 --- 3x²-10x+3=0 Δ=b²-4ac=(-10)²-4*3*3=100-36=64 √Δ=8 x₁=[-b-√Δ]/2a=[10-8]/6=1/3 x₂=[-b+√Δ]/2a=[10+8]/6=3
Zad.2 Rozłóż wielomian na czynniki: a) W(x) = -3x2 + 4x b) W(x) = x3 –x2 +9x-9 c) W(x) = 4x2 + 20x + 25 Zad.3 Rozwiąż równanie: a) x3 + 4x2 – 2x – 8 = 0 b) 3x4 – 10x3 + 10x – 3 = 0...
