What are the solutions to the equation x^4-6x^3-3x^2+24x-4=0 ?

The solutions to the equation x^4-6x^3-3x^2+24x-4=0 are x=-2,x=2,x=3+2sqrt(2),x=3-2sqrt(2)

Find the zeros of x^4-6x^3-3x^2+24x-4=0

The zeros of x^4-6x^3-3x^2+24x-4=0 are x=-2,x=2,x=3+2sqrt(2),x=3-2sqrt(2)

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x^{4} - 6 x^{3} - 3 x^{2} + 24 x - 4 = 0

x = - 2, x = 2, x = 3 + 22, x = 3 - 22

Decimal

x = - 2, x = 2, x = 5.82842 \dots, x = 0.17157 \dots

Solution steps

x^{4} - 6 x^{3} - 3 x^{2} + 24 x - 4 = 0

Factor

x^{4} - 6 x^{3} - 3 x^{2} + 24 x - 4 : (x + 2) (x - 2) (x^{2} - 6 x + 1)

(x + 2) (x - 2) (x^{2} - 6 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x - 2 = 0 or x^{2} - 6 x + 1 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 6 x + 1 = 0 : x = 3 + 22, x = 3 - 22

The solutions are

x = - 2, x = 2, x = 3 + 22, x = 3 - 22

x^{6} + 4 x^{3} + 8 = 0

x^{5} = x^{4}

x^{3} + 3 x^{2} - 4 x - 12 = 0

D, 2 b - hb = D^{3}

5 x^{4} - 9 x^{2} + 4

What are the solutions to the equation x^4-6x^3-3x^2+24x-4=0 ?
The solutions to the equation x^4-6x^3-3x^2+24x-4=0 are x=-2,x=2,x=3+2sqrt(2),x=3-2sqrt(2)
Find the zeros of x^4-6x^3-3x^2+24x-4=0
The zeros of x^4-6x^3-3x^2+24x-4=0 are x=-2,x=2,x=3+2sqrt(2),x=3-2sqrt(2)