What are the solutions to the equation 3x^4=81x ?

The solutions to the equation 3x^4=81x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2

Find the zeros of 3x^4=81x

The zeros of 3x^4=81x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2

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3 x^{4} = 81 x

x = 0, x = 3, x = - \frac{3}{2} + i \frac{3 3}{2}, x = - \frac{3}{2} - i \frac{3 3}{2}

Solution steps

3 x^{4} = 81 x

Move

81 x

to the left side

3 x^{4} - 81 x = 0

Factor

3 x^{4} - 81 x : 3 x (x - 3) (x^{2} + 3 x + 9)

3 x (x - 3) (x^{2} + 3 x + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0 or x^{2} + 3 x + 9 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 3 x + 9 = 0 : x = - \frac{3}{2} + i \frac{3 3}{2}, x = - \frac{3}{2} - i \frac{3 3}{2}

The solutions are

x = 0, x = 3, x = - \frac{3}{2} + i \frac{3 3}{2}, x = - \frac{3}{2} - i \frac{3 3}{2}

- x^{3} + 9 x^{2} - 15 x + 7 = 0

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

x^{4} + 27 x = 0

x^{4} - 4 x^{3} + 15 x^{2} - 4 x + 14 = 0

(x) (2 x)^{2} = 3.2 \cdot 1 0^{- 8}

What are the solutions to the equation 3x^4=81x ?
The solutions to the equation 3x^4=81x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2
Find the zeros of 3x^4=81x
The zeros of 3x^4=81x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2