What are the solutions to the equation roots x^4-729x ?

The solutions to the equation roots x^4-729x are x=0,x=9,x=-9/2+(9sqrt(3))/2 i,x=-9/2-(9sqrt(3))/2 i

Find the zeros of roots x^4-729x

The zeros of roots x^4-729x are x=0,x=9,x=-9/2+(9sqrt(3))/2 i,x=-9/2-(9sqrt(3))/2 i

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roots

x^{4} - 729 x

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

Solution steps

x^{4} - 729 x

The roots are the intercepts with the x-axis

(y = 0)

x^{4} - 729 x = 0

Factor

x^{4} - 729 x : x (x^{3} - 729)

x (x^{3} - 729) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 729 = 0

Solve

x^{3} - 729 = 0 : x = 9, x = - \frac{9}{2} + \frac{9 3}{2} i, x = - \frac{9}{2} - \frac{9 3}{2} i

The solutions are

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

7 x^{2} - 144 = - x^{4}

x^{3} - 13 x^{2} + 52 x - 60 = 0

- x^{3} + 14 x^{2} - 59 x + 70 = 0

y, 4 x^{3} - 16 y = 0

x^{4} - x^{2} + (\frac{1}{4}) = 0

What are the solutions to the equation roots x^4-729x ?
The solutions to the equation roots x^4-729x are x=0,x=9,x=-9/2+(9sqrt(3))/2 i,x=-9/2-(9sqrt(3))/2 i
Find the zeros of roots x^4-729x
The zeros of roots x^4-729x are x=0,x=9,x=-9/2+(9sqrt(3))/2 i,x=-9/2-(9sqrt(3))/2 i