Question

rowiąż równania:
a) x^3+2x^2-15x=0
b) x^3+3x^2-3x-9=0
c) x^4-5x^2-36=0

Answer 1

a) x^3 + 2x^2 - 15x = 0

x(x^2 + 2x - 15) = 0

x = 0      delta = 4 + 60 = 64

            pierw. z delty = 8

            x1 = -2-8/2 = -10/2 = -5
            x2 = -2 + 8 / 2 = 6/2 = 3

b) x^3 + 3x^2 - 3x - 9 = 0

x(x^2 + 3x) - 3(x - 3) = 0

(x-3)(x^2 + 3x) = 0

x - 3 = 0

x = 3

 

delta= 9 - 0 = 9

pierw. z delty = 3

x1 = -3 - 3 / 2 = -6/2 = -3

x2 = -3 + 3 / 2 - 0/2 = 0

 

c)

 

x^4 - 5x^2 - 36 = 0

x^2(x^2 - 5)  - 36 = 0

(x^2 - 36)(x^2 - 5) = 0

 

x^2 - 36 = 0

x^2 = 36

x=  6 lub x=-6

 

x^2 - 5 = 0

x^2 = 5

x = pierw. z 5 lub x = - pierw. z 5