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 Notation

x = - 2, x = 2, x = - 0.17157 \dots, x = - 5.82842 \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^{4} - 6 x^{3} + 2 x^{2} + 26 x + 17

9 x^{3} + 9 x^{2} - x - 1 = 0

4 x^{3} - 2 x^{2} - 14 x - 48

x^{5} - 6 x^{4} + 10 x^{3} - 6 x^{2} + 9 x = 0

2 x^{3} + 7 x^{2} - 2 x - 7 = 0

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)