What are the solutions to the equation x^3-3x^2+9x-27=0 ?

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

Find the zeros of x^3-3x^2+9x-27=0

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

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

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

3 x^{4} = 81 x

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

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

x^{4} + 27 x = 0

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