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

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

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

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

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

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

Decimal Notation

x = 0, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

4 x^{3} + 3 = 0

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

(12 - 3 x) \cdot (2 x - 1) x = 0

x^{3} - 0.75 x - 0.25 = 0

- λ^{3} + 5 λ^{2} = 0

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