What are the solutions to the equation 6x^3-11x^2-9x-1=0 ?

The solutions to the equation 6x^3-11x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(61))/6 ,x=(7-sqrt(61))/6

Find the zeros of 6x^3-11x^2-9x-1=0

The zeros of 6x^3-11x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(61))/6 ,x=(7-sqrt(61))/6

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6 x^{3} - 11 x^{2} - 9 x - 1 = 0

x = - \frac{1}{2}, x = \frac{7 + 61}{6}, x = \frac{7 - 61}{6}

Decimal Notation

x = - 0.5, x = 2.46837 \dots, x = - 0.13504 \dots

Solution steps

6 x^{3} - 11 x^{2} - 9 x - 1 = 0

Factor

6 x^{3} - 11 x^{2} - 9 x - 1 : (2 x + 1) (3 x^{2} - 7 x - 1)

(2 x + 1) (3 x^{2} - 7 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or 3 x^{2} - 7 x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

3 x^{2} - 7 x - 1 = 0 : x = \frac{7 + 61}{6}, x = \frac{7 - 61}{6}

The solutions are

x = - \frac{1}{2}, x = \frac{7 + 61}{6}, x = \frac{7 - 61}{6}

30 x^{4} - 120 x^{3} = 0

4 x^{3} - 12 x^{2} - 9 x - 1 = 0

2 x^{3} + 3 x^{2} - 12 x + 1 = 0

x^{3} - 2 x^{2} - 25 x + 50 = 0

H^{3} - 0.479 H^{2} + 0.01 = 0

What are the solutions to the equation 6x^3-11x^2-9x-1=0 ?
The solutions to the equation 6x^3-11x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(61))/6 ,x=(7-sqrt(61))/6
Find the zeros of 6x^3-11x^2-9x-1=0
The zeros of 6x^3-11x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(61))/6 ,x=(7-sqrt(61))/6