What are the solutions to the equation x^3-3x^2+3x-65=0 ?

The solutions to the equation x^3-3x^2+3x-65=0 are x=5,x=-1+2sqrt(3)i,x=-1-2sqrt(3)i

Find the zeros of x^3-3x^2+3x-65=0

The zeros of x^3-3x^2+3x-65=0 are x=5,x=-1+2sqrt(3)i,x=-1-2sqrt(3)i

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x^{3} - 3 x^{2} + 3 x - 65 = 0

x = 5, x = - 1 + 23 i, x = - 1 - 23 i

Solution steps

x^{3} - 3 x^{2} + 3 x - 65 = 0

Factor

x^{3} - 3 x^{2} + 3 x - 65 : (x - 5) (x^{2} + 2 x + 13)

(x - 5) (x^{2} + 2 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{2} + 2 x + 13 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{2} + 2 x + 13 = 0 : x = - 1 + 23 i, x = - 1 - 23 i

The solutions are

x = 5, x = - 1 + 23 i, x = - 1 - 23 i

(x^{2} + 6)^{2} = 0

32 = 4 x^{3}

k + k^{3} = 68

z^{3} + 2 z^{2} + 21 z + 58 = 0

(x - 7)^{3} = 13

What are the solutions to the equation x^3-3x^2+3x-65=0 ?
The solutions to the equation x^3-3x^2+3x-65=0 are x=5,x=-1+2sqrt(3)i,x=-1-2sqrt(3)i
Find the zeros of x^3-3x^2+3x-65=0
The zeros of x^3-3x^2+3x-65=0 are x=5,x=-1+2sqrt(3)i,x=-1-2sqrt(3)i