What are the solutions to the equation 12x^3-20x^2-5x+1=0 ?

The solutions to the equation 12x^3-20x^2-5x+1=0 are x=-1/3 ,x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2

Find the zeros of 12x^3-20x^2-5x+1=0

The zeros of 12x^3-20x^2-5x+1=0 are x=-1/3 ,x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2

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12 x^{3} - 20 x^{2} - 5 x + 1 = 0

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

Solution steps

12 x^{3} - 20 x^{2} - 5 x + 1 = 0

Factor

12 x^{3} - 20 x^{2} - 5 x + 1 : (3 x + 1) (4 x^{2} - 8 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

4 x^{2} - 8 x + 1 = 0 : x = \frac{2 + 3}{2}, x = \frac{2 - 3}{2}

The solutions are

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

4 x^{4} - 125 x^{2} + 625 = 0

x^{3} + 2 x^{2} = 36 x + 72

9 x^{3} - 27 x^{2} - 25 x + 75 = 0

- 34 x^{3} - 21 x^{2} - 30 x = 0

(3 p - 4)^{6} = 64

What are the solutions to the equation 12x^3-20x^2-5x+1=0 ?
The solutions to the equation 12x^3-20x^2-5x+1=0 are x=-1/3 ,x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2
Find the zeros of 12x^3-20x^2-5x+1=0
The zeros of 12x^3-20x^2-5x+1=0 are x=-1/3 ,x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2