Równania wielomianowe

[hojrak]

a) \(x^3-7x-4x+28=0\)
b) \(x^3-3x^2+2x-6=0\)
c) \(x^3-6x^2-9x+54=0\)
d) \(x^3+2x^2-8x-16=0\)
e) \(3x^3-4x^2-3x+4=0\)
f) \(x^3-6x^2-12x+72=0\)
g) \(9x^3+18x^2-4x-8=0\)
h) \(x^3-6x^2-11x+66=0\)
i) \(4x^3+4x^2-x-1=0\)
j) \(x^4-2x^3+27x-54=0\)
k) \(8x^3+8x^2-3x-3=0\)
l) \(x^3+3x^2+2x+6=0\)
m) \(x^3-7x^2-4x+28=0\)

[eresh]

a) \(x^3-7x-4x+28=0\)

Na pewno to tak wygląda?

[eresh]

b) \(x^3-3x^2+2x-6=0\)

\(x^3-3x^2+2x-6=0\\
x^2(x-3)+2(x-3)=0\\
(x-3)(x^2+2)=0\\
x=3\)

[hojrak]

a) \(x^3-7x-4x+28=0\)

Na pewno to tak wygląda?

\(x^3-7x^2-4x+28=0\)

[eresh]

c) \(x^3-6x^2-9x+54=0\)

\(x^2(x-6)-9(x-6)=0\\
(x-6)(x^2-9)=0\\
(x-6)(x-3)(x+3)=0\\
x=6\\
x=3\\
x=-3\)

[eresh]

d) \(x^3+2x^2-8x-16=0\)

\(x^2(x+2)-8(x+2)=0\\
(x+2)(x^2-8)=0\\
(x+2)(x-2\sqrt{2})(x+2\sqrt{2})=0\\
x=-2\\
x=-2\sqrt{2}\\
x=2\sqrt{2}\)

[eresh]

e) \(3x^3-4x^2-3x+4=0\)

\(x^2(3x-4)-(2x-4)=0\\
(3x-4)(x^2-1)=0\\
(3x-4)(x-1)(x+1)=0\\
x=\frac{4}{3}\\
x=1\\
x=-1\)

[eresh]

f) \(x^3-6x^2-12x+72=0\)

\(x^2(x-6)-12(x-6)=0\\
(x-6)(x^2-12)=0\\
x=6\\
x=2\sqrt{3}\\
x=-2\sqrt{3}\)

[eresh]

g) \(9x^3+18x^2-4x-8=0\)

\(9x^2(x+2)-4(x+2)=0\\
(3x-2)(3x+2)(x+2)=0\\
x=\frac{2}{3}\\
x=-\frac{2}{3}\\
x=-2\)

[eresh]

h) \(x^3-6x^2-11x+66=0\)

\(x^2(x-6)-11(x-6)=0\\
(x-6)(x-\sqrt{11})(x+\sqrt{11})=0\\
x=6\\
x=\sqrt{11}\
x=-\sqrt{11}\)

[eresh]

i) \(4x^3+4x^2-x-1=0\)

\(4x^2(x+1)-(x+1)=0\\
(x+1)(2x-1)(2x+1)=0\\
x=-1\\
x=\frac{1}{2}\\
x=-\frac{1}{2}\)

[eresh]

j) \(x^4-2x^3+27x-54=0\)

\(x^3(x-2)+27(x-2)=0\\
(x-2)(x^3+27)=0\\
x=2\\
x^3=-27\So x=-3\)

[eresh]

k) \(8x^3+8x^2-3x-3=0\)

\(8x^2(x+1)-3(x+1)=0\\
(x+1)(8x^2-3)=0\\
x=-1\\
8x^2=3\\
x^2=\frac{3}{8}\\
x=-\frac{\sqrt{3}}{2\sqrt{2}}\\
x=\frac{\sqrt{3}}{2\sqrt{2}}\)
usuń niewymierność z mianownika

[eresh]

l) \(x^3+3x^2+2x+6=0\)

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

[eresh]

m) \(x^3-7x^2-4x+28=0\)

\(x^2(x-7)-4(x-7)=0\\
(x-7)(x^2-4)=0\\
(x-7)(x-2)(x+2)=0\\
x=7\\
x=2\\
x=-2\)