What are the solutions to the equation x^3-4x^2-6x+9=0 ?

The solutions to the equation x^3-4x^2-6x+9=0 are x=1,x=(3+3sqrt(5))/2 ,x=(3-3sqrt(5))/2

Find the zeros of x^3-4x^2-6x+9=0

The zeros of x^3-4x^2-6x+9=0 are x=1,x=(3+3sqrt(5))/2 ,x=(3-3sqrt(5))/2

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x^{3} - 4 x^{2} - 6 x + 9 = 0

x = 1, x = \frac{3 + 3 5}{2}, x = \frac{3 - 3 5}{2}

Decimal Notation

x = 1, x = 4.85410 \dots, x = - 1.85410 \dots

Solution steps

x^{3} - 4 x^{2} - 6 x + 9 = 0

Factor

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

(x - 1) (x^{2} - 3 x - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 3 x - 9 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 3 x - 9 = 0 : x = \frac{3 + 3 5}{2}, x = \frac{3 - 3 5}{2}

The solutions are

x = 1, x = \frac{3 + 3 5}{2}, x = \frac{3 - 3 5}{2}

5 z^{2} - 45 = 8 z^{3} - 72 z

x^{3} - 9 x^{2} + 36 x - 36 = 0

x^{3} - 7 x^{2} + 36 = 0

3 x^{4} + 4 x^{3} - 6 x^{2} - 12 x = 0

16 z^{4} = 1

What are the solutions to the equation x^3-4x^2-6x+9=0 ?
The solutions to the equation x^3-4x^2-6x+9=0 are x=1,x=(3+3sqrt(5))/2 ,x=(3-3sqrt(5))/2
Find the zeros of x^3-4x^2-6x+9=0
The zeros of x^3-4x^2-6x+9=0 are x=1,x=(3+3sqrt(5))/2 ,x=(3-3sqrt(5))/2