What are the solutions to the equation 2x=λ*4x^3 ?

The solutions to the equation 2x=λ*4x^3 are x=0,x= 1/(sqrt(2λ)),x=-1/(sqrt(2λ));\quad λ\ne 0

Find the zeros of 2x=λ*4x^3

The zeros of 2x=λ*4x^3 are x=0,x= 1/(sqrt(2λ)),x=-1/(sqrt(2λ));\quad λ\ne 0

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2 x = λ \cdot 4 x^{3}

x = 0, x = \frac{1}{2 λ}, x = - \frac{1}{2 λ}; λ \neq = 0

Solution steps

2 x = λ \cdot 4 x^{3}

Move

λ \cdot 4 x^{3}

to the left side

2 x - λ \cdot 4 x^{3} = 0

Factor

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

2 x (1 - 2 λ x^{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 1 - 2 λ x^{2} = 0

Solve

1 - 2 λ x^{2} = 0 : x = \frac{1}{2 λ}, x = - \frac{1}{2 λ}; λ \neq = 0

The solutions are

x = 0, x = \frac{1}{2 λ}, x = - \frac{1}{2 λ}; λ \neq = 0

0.15 = (1 + \frac{x}{12})^{12} - 1

9 x^{3} + 54 x^{2} = x + 6

- 4 x^{3} + 6 x - 1 = 0

38 = h (2 h^{2} - 3 h)

(y - 1) (y^{2} + y + 2) = 0

What are the solutions to the equation 2x=λ*4x^3 ?
The solutions to the equation 2x=λ*4x^3 are x=0,x= 1/(sqrt(2λ)),x=-1/(sqrt(2λ));\quad λ\ne 0
Find the zeros of 2x=λ*4x^3
The zeros of 2x=λ*4x^3 are x=0,x= 1/(sqrt(2λ)),x=-1/(sqrt(2λ));\quad λ\ne 0