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

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

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

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

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

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

Solution steps

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

Factor

x^{3} - 3 x^{2} + x - 3 : (x - 3) (x^{2} + 1)

(x - 3) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 1 = 0

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

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

x^{3} + 2 x + 1 = 0

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

x^{3} + x^{2} - 12 x = 0

x^{4} - 10 x^{2} + 25 = 0

x^{3} = 70

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