What are the solutions to the equation 4x^3-6x+2=0 ?

The solutions to the equation 4x^3-6x+2=0 are x=1,x=(-1+sqrt(3))/2 ,x=-(1+sqrt(3))/2

Find the zeros of 4x^3-6x+2=0

The zeros of 4x^3-6x+2=0 are x=1,x=(-1+sqrt(3))/2 ,x=-(1+sqrt(3))/2

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

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

Decimal

x = 1, x = 0.36602 \dots, x = - 1.36602 \dots

Solution steps

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

Factor

4 x^{3} - 6 x + 2 : 2 (x - 1) (2 x^{2} + 2 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

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

12 x^{2} + 48 x = - x^{3} - 64

0.75 = 10 x^{9} - 9 x^{10}

x^{4} - 2 x^{2} + 6 = 0

4 x^{3} - 9 x^{2} + 4 = 0

a^{6} = 30

What are the solutions to the equation 4x^3-6x+2=0 ?
The solutions to the equation 4x^3-6x+2=0 are x=1,x=(-1+sqrt(3))/2 ,x=-(1+sqrt(3))/2
Find the zeros of 4x^3-6x+2=0
The zeros of 4x^3-6x+2=0 are x=1,x=(-1+sqrt(3))/2 ,x=-(1+sqrt(3))/2