1)(x²+5x+6)(10-x)=0 x²+5x+6=0 lub 10-x=0 Δ=b²-4ac -x=-10 Δ=25-4*1*6 x=10 Δ=25 -24 Δ=1 √Δ1 x1=(-b-√Δ)/2a x2=(-b+√Δ)/2a x1=(-5-1)/2*1 x2=(-5+1)/2*1 x1= -3 x2=-2 pierwiastkami tego równania są x=-3; x=-2; x=10 zad2 x⁴+4x³-5x²=0 x²(x²+4x-5)=0 x²=0 lub x²+4x-5=0 x=0 Δ=16-4*(-5) Δ=36 √Δ=6 x1=(-4-6)/2*1 x2=(-4+6)/2*1 x1=-5 x2=1 x∈{-5;0;1} zad3 x⁵-2x³=0 x³(x²-2)=0 x³=0 lub x²-2=0 x=0 x²=2 x=-√2 x=√2 rozwiązaniem tego równania są liczby: x=-√2; x=0 ; x=√2 zad4 W(x)= 3x³-5x²-6x+10 3x³-5x²-6x-10=0 x²(3x-5)-2(3x-5)=0 (3x-5)(x²-2)=0 3x-5=0 lub x²-2)=0 3x=5 x²=2 x=3/5 x=-√2 x=√2 pierwiastkami tego wielomianu są liczby x=3/5; x=-√2; x=√2
1. (x² + 5x + 6)(10 - x) = 0 (x² + 2x + 3x + 6)(10 - x) = 0 [x(x + 2) + 3(x + 2)](10 - x) = 0 (x + 2)(x + 3)(10 - x) = 0 x + 2 = 0 v x + 3 = 0 v 10 - x = 0 x = -2 v x = -3 v x = 10 x ∈ {-3;-2;10} 2) x⁴ + 4x³ - 5x² = 0 x²(x² + 4x - 5) = 0 x²(x² - x + 5x - 5) = 0 x²[x(x - 1) + 5(x - 1)] = 0 x²(x - 1)(x + 5) = 0 x² = 0 v x - 1 = 0 v x + 5 = 0 x = 0 v x = 1 v x = -5 x ∈ {-5;0;1} 3. x⁵ - 2x³ = 0 x³(x² - 2) = 0 x³(x + √2)(x - √2) = 0 x³ = 0 v x + √2 = 0 v x - √2 = 0 x = 0 v x = -√2 v x = √2 x ∈ {-√2;0;√2} 4. W(x) = 3x³ - 5x² - 6x + 10 W(x) = 0 3x³ - 5x² - 6x + 10 = 0 x²(3x - 5) - 2(3x - 5) = 0 (3x - 5)(x² - 2) = 0 (3x - 5)(x + √2)(x - √2) = 0 3x - 5 = 0 v x + √2 = 0 v x - √2 = 0 x = 5/3 v x = -√2 v x = √2 x ∈ {-√2;√2;5/3}
