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

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

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

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

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

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

Decimal Notation

x = - 3, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

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

Factor

x^{3} - x^{2} - 11 x + 3 : (x + 3) (x^{2} - 4 x + 1)

(x + 3) (x^{2} - 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

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

The solutions are

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

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

(x - 2)^{3} = 4

2 x^{3} - 6 x^{2} + 8 = 0

0 = x^{4} - 36

6 x^{3} + 36 x^{2} + 54 x = 0

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