What are the solutions to the equation (3x^8)*x^4=3x ?

The solutions to the equation (3x^8)*x^4=3x are x=0,x=1

Find the zeros of (3x^8)*x^4=3x

The zeros of (3x^8)*x^4=3x are x=0,x=1

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(3 x^{8}) \cdot x^{4} = 3 x

x = 0, x = 1

Solution steps

(3 x^{8}) x^{4} = 3 x

Move

3 x

to the left side

3 x^{8} x^{4} - 3 x = 0

Factor

3 x^{8} x^{4} - 3 x : 3 x (x - 1) (x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1)

3 x (x - 1) (x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0 :

No Solution for

x \in R

The solutions are

x = 0, x = 1

y^{4} = 9

x^{7} = 128

- 60 x^{3} + 30 x = 0

x^{5} + x^{3} + x = 2

x^{12} = 2

What are the solutions to the equation (3x^8)*x^4=3x ?
The solutions to the equation (3x^8)*x^4=3x are x=0,x=1
Find the zeros of (3x^8)*x^4=3x
The zeros of (3x^8)*x^4=3x are x=0,x=1