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

The solutions to the equation 4x^2-2x^3-2x^3-x^4=0 are x=0,x=2(sqrt(2)-1),x=-2(1+sqrt(2))

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

The zeros of 4x^2-2x^3-2x^3-x^4=0 are x=0,x=2(sqrt(2)-1),x=-2(1+sqrt(2))

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

x = 0, x = 2 (2 - 1), x = - 2 (1 + 2)

Decimal Notation

x = 0, x = 0.82842 \dots, x = - 4.82842 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or - 4 + 4 x + x^{2} = 0

Solve

- 4 + 4 x + x^{2} = 0 : x = 2 (2 - 1), x = - 2 (1 + 2)

The solutions are

x = 0, x = 2 (2 - 1), x = - 2 (1 + 2)

3 x^{3} + x^{2} - 38 x + 24 = 0

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

3018 = x^{4} - x^{3} - 7 x^{2} + 9 x

- x^{3} + 6 x^{2} - 12 x + 6 = 0

x^{4} - 3 4^{2} + 255 = 0

What are the solutions to the equation 4x^2-2x^3-2x^3-x^4=0 ?
The solutions to the equation 4x^2-2x^3-2x^3-x^4=0 are x=0,x=2(sqrt(2)-1),x=-2(1+sqrt(2))
Find the zeros of 4x^2-2x^3-2x^3-x^4=0
The zeros of 4x^2-2x^3-2x^3-x^4=0 are x=0,x=2(sqrt(2)-1),x=-2(1+sqrt(2))