What are the solutions to the equation 4x^3-12x^2-11x-2=0 ?

The solutions to the equation 4x^3-12x^2-11x-2=0 are x=-1/2 ,x=(7+sqrt(65))/4 ,x=(7-sqrt(65))/4

Find the zeros of 4x^3-12x^2-11x-2=0

The zeros of 4x^3-12x^2-11x-2=0 are x=-1/2 ,x=(7+sqrt(65))/4 ,x=(7-sqrt(65))/4

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4 x^{3} - 12 x^{2} - 11 x - 2 = 0

x = - \frac{1}{2}, x = \frac{7 + 65}{4}, x = \frac{7 - 65}{4}

Decimal Notation

x = - 0.5, x = 3.76556 \dots, x = - 0.26556 \dots

Solution steps

4 x^{3} - 12 x^{2} - 11 x - 2 = 0

Factor

4 x^{3} - 12 x^{2} - 11 x - 2 : (2 x + 1) (2 x^{2} - 7 x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

2 x^{2} - 7 x - 2 = 0 : x = \frac{7 + 65}{4}, x = \frac{7 - 65}{4}

The solutions are

x = - \frac{1}{2}, x = \frac{7 + 65}{4}, x = \frac{7 - 65}{4}

x^{5} = 64 x^{2}

- 16 x - 4 x^{3} = 164

20 x^{3} + 60 x^{2} = 0

x^{23} x + 2 = 0

2 x^{3} - 16 x^{2} - 40 x = 0

What are the solutions to the equation 4x^3-12x^2-11x-2=0 ?
The solutions to the equation 4x^3-12x^2-11x-2=0 are x=-1/2 ,x=(7+sqrt(65))/4 ,x=(7-sqrt(65))/4
Find the zeros of 4x^3-12x^2-11x-2=0
The zeros of 4x^3-12x^2-11x-2=0 are x=-1/2 ,x=(7+sqrt(65))/4 ,x=(7-sqrt(65))/4