What are the solutions to the equation x^3-6x^2+9x-2=0 ?

The solutions to the equation x^3-6x^2+9x-2=0 are x=2,x=2+sqrt(3),x=2-sqrt(3)

Find the zeros of x^3-6x^2+9x-2=0

The zeros of x^3-6x^2+9x-2=0 are x=2,x=2+sqrt(3),x=2-sqrt(3)

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x^{3} - 6 x^{2} + 9 x - 2 = 0

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

Decimal Notation

x = 2, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x^{3} - 6 x^{2} + 9 x - 2 = 0

Factor

x^{3} - 6 x^{2} + 9 x - 2 : (x - 2) (x^{2} - 4 x + 1)

(x - 2) (x^{2} - 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - 4 x + 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

The solutions are

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

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

4 x^{3} + 4 x^{2} - 7 x + 2 = 0

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

16 x - 64 x^{3} = 0

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

What are the solutions to the equation x^3-6x^2+9x-2=0 ?
The solutions to the equation x^3-6x^2+9x-2=0 are x=2,x=2+sqrt(3),x=2-sqrt(3)
Find the zeros of x^3-6x^2+9x-2=0
The zeros of x^3-6x^2+9x-2=0 are x=2,x=2+sqrt(3),x=2-sqrt(3)