What are the solutions to the equation x^3-3x^2-9x+11=0 ?

The solutions to the equation x^3-3x^2-9x+11=0 are x=1,x=1+2sqrt(3),x=1-2sqrt(3)

Find the zeros of x^3-3x^2-9x+11=0

The zeros of x^3-3x^2-9x+11=0 are x=1,x=1+2sqrt(3),x=1-2sqrt(3)

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x^{3} - 3 x^{2} - 9 x + 11 = 0

x = 1, x = 1 + 23, x = 1 - 23

Decimal Notation

x = 1, x = 4.46410 \dots, x = - 2.46410 \dots

Solution steps

x^{3} - 3 x^{2} - 9 x + 11 = 0

Factor

x^{3} - 3 x^{2} - 9 x + 11 : (x - 1) (x^{2} - 2 x - 11)

(x - 1) (x^{2} - 2 x - 11) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 2 x - 11 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 2 x - 11 = 0 : x = 1 + 23, x = 1 - 23

The solutions are

x = 1, x = 1 + 23, x = 1 - 23

x x^{2} + 6 x + 8 = 0

x^{3} - 28 = 100

x^{4} - 8 x^{2} + 1 = 0

x, y + 7 = 3 x^{3}

(x^{2} - 6 x + 9)^{2} = 0

What are the solutions to the equation x^3-3x^2-9x+11=0 ?
The solutions to the equation x^3-3x^2-9x+11=0 are x=1,x=1+2sqrt(3),x=1-2sqrt(3)
Find the zeros of x^3-3x^2-9x+11=0
The zeros of x^3-3x^2-9x+11=0 are x=1,x=1+2sqrt(3),x=1-2sqrt(3)