What are the solutions to the equation x^4=27x ?

The solutions to the equation x^4=27x are x=0,x=3,x=-3/2+(3sqrt(3))/2 i,x=-3/2-(3sqrt(3))/2 i

Find the zeros of x^4=27x

The zeros of x^4=27x are x=0,x=3,x=-3/2+(3sqrt(3))/2 i,x=-3/2-(3sqrt(3))/2 i

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x^{4} = 27 x

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

Solution steps

x^{4} = 27 x

Move

27 x

to the left side

x^{4} - 27 x = 0

Factor

x^{4} - 27 x : x (x^{3} - 27)

x (x^{3} - 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 27 = 0

Solve

x^{3} - 27 = 0 : x = 3, x = - \frac{3}{2} + \frac{3 3}{2} i, x = - \frac{3}{2} - \frac{3 3}{2} i

The solutions are

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

7 x^{4} = 56 x

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

x^{4} + 3 x^{2} - 28 = 0

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

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

What are the solutions to the equation x^4=27x ?
The solutions to the equation x^4=27x are x=0,x=3,x=-3/2+(3sqrt(3))/2 i,x=-3/2-(3sqrt(3))/2 i
Find the zeros of x^4=27x
The zeros of x^4=27x are x=0,x=3,x=-3/2+(3sqrt(3))/2 i,x=-3/2-(3sqrt(3))/2 i