Question

Rozwiąż równanie;
a). 4x^2+x-3=0
b). (3x-12)(x+2)(x-1)=0
c). x^4-3x^3-4x^2=0

Answer 1

A). 4x²+x-3=0
Δ=b²-4ac=1+48=49
x₁=(-b+√Δ) /2a = -1+7/8 = 6/8 = 3/4
x₂=(-b+√Δ) /2a = -1-7/8 = -8/8 = -1
b). (3x-12)(x+2)(x-1)=0
3x₁=12
x₁=4
x₂=-2
x₃=1
c). x⁴-3x³-4x²=0
x²(x²-3x-4)=0
x₁=0 pierwiastek podwójny
Δ=b²-4ac=9+16=25
x₂=(-b+√Δ) /2a = 3+5/2 = 8/2 = 4
x₃=(-b+√Δ) /2a = 3-5/2 = -2/2 = -1

Answer 2

A). 4x^2+x-3=0
a=4 b=1 c=-3
delta=b^2 -4ac=1+48=49
x1=-b-pierwiastek z delty/2a=-1-7/8=-8/8=-1
x2=-b+pierwiastek z delty/20=-1+7/8=6/8=0,75

b). (3x-12)(x+2)(x-1)=0
(6x+3x^2-12x-24)(x-1)=0
(3x^2-6x-24)(x-1)=0
3x^3-3x^2-6x^2+6x-24x+24=
3x^3-8x^2-18x+24=0
x^2(3x-8)-6(3x-8)=0
(x^2-6)(3x-8)=0
(x^2-6)=0 v(3x-8)=0
x^2=6 v 3x=8
x=pierwiastek z 6 v x=- pierwiastek z 6 v x=2 i 2/3

c). x^4-3x^3-4x^2=0
x^2(x^2-3x-4)=0
x^2=0 v (x^2-3x-4)=0
x=o v a=1 b=-3 c=-4
delta=b^2 - 4ac= 9+16=25
x1=-b-pierwiastek z delty/2a=-3-5/2=-4
x2=-b+pierwiastek z delty/2a=-3+5/2=1

x=0 v x=-4 v x=1