What are the solutions to the equation 5x^4=135x ?

The solutions to the equation 5x^4=135x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2

Find the zeros of 5x^4=135x

The zeros of 5x^4=135x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2

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5 x^{4} = 135 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

5 x^{4} = 135 x

Move

135 x

to the left side

5 x^{4} - 135 x = 0

Factor

5 x^{4} - 135 x : 5 x (x - 3) (x^{2} + 3 x + 9)

5 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}

6 n^{4} + 9 n^{3} + 3 n^{2} = 0

x^{5} = 16

- x^{3} - 4 x^{2} + 16 x + 64 = 0

x^{3} + 6 x^{2} + 9 x + 9 = 0

(x - 2) (x - 5 i) (x + 5 i) = 52

What are the solutions to the equation 5x^4=135x ?
The solutions to the equation 5x^4=135x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2
Find the zeros of 5x^4=135x
The zeros of 5x^4=135x are x=0,x=3,x=-3/2+i(3sqrt(3))/2 ,x=-3/2-i(3sqrt(3))/2