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

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

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

The zeros of x^4-x^2=3x^3-3x are x=0,x=3,x=-1,x=1

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

x = 0, x = 3, x = - 1, x = 1

Solution steps

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

Move

3 x

to the left side

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

Move

3 x^{3}

to the left side

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

Factor

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

x (x - 3) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0 or x + 1 = 0 or x - 1 = 0

Solve

x - 3 = 0 : x = 3

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = 3, x = - 1, x = 1

m^{4} - 2 m^{2} - 8 = 0

(x + 3)^{4} + 2 (x + 3)^{2} - 8 = 0

x^{3} + 3 x^{2} - 112 = 0

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

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

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