What are the solutions to the equation roots x^3-9x^2+31x-39 ?

The solutions to the equation roots x^3-9x^2+31x-39 are x=3,x=3+2i,x=3-2i

Find the zeros of roots x^3-9x^2+31x-39

The zeros of roots x^3-9x^2+31x-39 are x=3,x=3+2i,x=3-2i

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roots

x^{3} - 9 x^{2} + 31 x - 39

x = 3, x = 3 + 2 i, x = 3 - 2 i

Solution steps

x^{3} - 9 x^{2} + 31 x - 39

The roots are the intercepts with the x-axis

(y = 0)

x^{3} - 9 x^{2} + 31 x - 39 = 0

Factor

x^{3} - 9 x^{2} + 31 x - 39 : (x - 3) (x^{2} - 6 x + 13)

(x - 3) (x^{2} - 6 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} - 6 x + 13 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 6 x + 13 = 0 : x = 3 + 2 i, x = 3 - 2 i

The solutions are

x = 3, x = 3 + 2 i, x = 3 - 2 i

4 x^{3} - 18 x^{2} + 24 x = 0

x^{3} - 2 - 2 \times i = 0

4 x^{3} - 57 x^{2} + 252 x - 324 = 0

0 = c x (x - 1)^{2} - x

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

What are the solutions to the equation roots x^3-9x^2+31x-39 ?
The solutions to the equation roots x^3-9x^2+31x-39 are x=3,x=3+2i,x=3-2i
Find the zeros of roots x^3-9x^2+31x-39
The zeros of roots x^3-9x^2+31x-39 are x=3,x=3+2i,x=3-2i