Question

Rozwiąż równanie wielomianowe: a)x⁴-1=0 b)x³-3x²-4x-12=0 c)3x³-7x²-7x+3=0

Answer 1

a)

x^4 - 1 = 0

x^4 = 1

rozw. x = 1 v x = -1

b) x^3 - 3x^2 - 4x - 12 = 0

x(x^2 - 3x - 4) - 12 = 0

liczymy delte z nawiasu wiec
d - niech to bedzie delta
d = b^2 - 4ac
d = 9 - 4 * 1 * -4
d = 9 + 16 = 25
sqrt d = 5

x1 = -b - sqrt d/2a = 3 - 5 / 2 = -1
x2 = -b + sqrt d/2a = 3 + 5 / 2 = 4

wiec nasze rownanie ma postac
x(x+1)(x-4) - 12=0

rozw . x=12 v x=0 v x=-1 v x=4

 

 

c)
3x^3 - 7x^2 - 7x +3 = 0
x(3x^2 - 7x - 7) + 3 = 0
liczymy delte

d = b^2 - 4ac
d = 49 + 84
d = sqrt z 133

x1 = 7 - sqrt133/6
x2 = 7 + sqrt133/6

rozw. x=-3 v x=0 x=-7-sqrt133/6 v x=7+sqrt133/6