What are the solutions to the equation 3x^4-9x^3=-9x^2+27x ?

The solutions to the equation 3x^4-9x^3=-9x^2+27x are x=0,x=3,x=sqrt(3)i,x=-sqrt(3)i

Find the zeros of 3x^4-9x^3=-9x^2+27x

The zeros of 3x^4-9x^3=-9x^2+27x are x=0,x=3,x=sqrt(3)i,x=-sqrt(3)i

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3 x^{4} - 9 x^{3} = - 9 x^{2} + 27 x

x = 0, x = 3, x = 3 i, x = - 3 i

Solution steps

3 x^{4} - 9 x^{3} = - 9 x^{2} + 27 x

Move

27 x

to the left side

3 x^{4} - 9 x^{3} - 27 x = - 9 x^{2}

Move

9 x^{2}

to the left side

3 x^{4} - 9 x^{3} - 27 x + 9 x^{2} = 0

Factor

3 x^{4} - 9 x^{3} - 27 x + 9 x^{2} : 3 x (x - 3) (x^{2} + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

x = 0, x = 3, x = 3 i, x = - 3 i

0 = 4 x^{3} - 24 x^{2} - x + 6

x^{3} + 7 x + 6 = 0

z^{4} = 196

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

y^{4} = 169

What are the solutions to the equation 3x^4-9x^3=-9x^2+27x ?
The solutions to the equation 3x^4-9x^3=-9x^2+27x are x=0,x=3,x=sqrt(3)i,x=-sqrt(3)i
Find the zeros of 3x^4-9x^3=-9x^2+27x
The zeros of 3x^4-9x^3=-9x^2+27x are x=0,x=3,x=sqrt(3)i,x=-sqrt(3)i