Question

Rozłóż wielomian na czynniki:

a) W(x)=

b) Q(x)=

c) V(x)=

Answer 1

a) W(x)= = -5(x-2)(x -3/5)

 

  W(x) = -5x² +13x -6

  W(x) = a( x - x1)(x -x2)  - postać iloczynowa

a = -5

b = 13

c = -6

∆ = b² - 4ac = (13)² -4*(-5) *(-6) = 169 - 120 = 49

√∆ = √49 = 7

x1= (-b - √∆):2a = (-13 -7):2*(-5) = (-20) : (-10) = 2

x2 =(-b + √∆):2a = (-13 +7):2*(-5) = (-6) : (-10) = 6/10 = 3/5

W(x) = -5( x -2)(x -3/5)

     

 

b) Q(x)=

    Q(x) = 2(3x²  -2) = 2(x√3 -√2)(x√3 + √2)

 

c) V(x)=

   V(x) = 9x² -24 x +16  = (3x +4)² = (3x +4)(3x+4)

lub

a = 9

b = -24

c = 16

Δ = b² - 4 *a*c = (-24)² - 4*9*16  = 576 - 576 = 0

x1 = x2 = (-b):2a = [-(-24)] : 2*9 = 24 :18 = 4/3

V(x) = a(x -x1)(x- x2)

V(x) = 9(x -4/3)(x-4/3)

 

Answer 2