Odpowiedź:
b)
w(x) = 4x⁵ - 6x⁴ - 10x³ = x³(4x² - 6x - 10)
4x² - 6x - 10 = 0
a = 4 , b = - 6 , c = - 10
Δ = b² - 4ac = (- 6)² - 4 * 4 * (- 10) = 36 + 160 = 196
√Δ = √196 = 14
x₁ = ( - b - √Δ)/2a = ( 6 - 14)/8 = - 8/8 = - 1
x₂ = (- b + √Δ)/2a = (6 + 14)/8 = 20/8 = 2 4/8 = 2 1/2 = 2,5
w(x) = x³(x + 1)(x - 2,5)
c)
w(x)= 2x⁶ + 3x⁵ - 2x⁴ = x⁴(2x²+3x -2)
2x² + 3x - 2 = 0
a= 2 , b = 3 , c = - 2
Δ = b² - 4ac = 3² - 4 * 2 * ( - 2) = 9 + 16 = 25
√Δ = √25 = 5
x₁ = ( - b - √Δ)/2a = ( - 3 - 5)/4= -8/4 = - 2
x₂ = (- b + √Δ)/2a = (- 3 + 5)/4 = 2/4 = 1/2 = 0,5
w(x) = x⁴(x+2)(x - 0,5)
c)
w(x) = 6x⁷ - 8x⁶ - 8x⁵ = 2x⁵(3x² - 4x - 4)
3x² - 4x - 4 = 0
a = 3 , b = - 4 , c = - 4
Δ = b² - 4ac = (- 4)² - 4 * 3 * (- 4) = 16 + 48 = 64
√Δ = √64 = 8
x₁ = ( - b - √Δ)/2a = ( 4 - 8)/6 = -2/6 = - 1/3
x₂ = (- b + √Δ)/2a = (4 + 8)/6 = 12/6 = 2
w(x) = 2x⁵(x+1/3)(x - 2 )
