What are the solutions to the equation roots 3x^2-12x+8 ?

The solutions to the equation roots 3x^2-12x+8 are x=(2(3+sqrt(3)))/3 ,x=(2(3-sqrt(3)))/3

Find the zeros of roots 3x^2-12x+8

The zeros of roots 3x^2-12x+8 are x=(2(3+sqrt(3)))/3 ,x=(2(3-sqrt(3)))/3

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roots

3 x^{2} - 12 x + 8

x = \frac{2 ( 3 + 3 )}{3}, x = \frac{2 ( 3 - 3 )}{3}

Solution steps

3 x^{2} - 12 x + 8

The roots are the intercepts with the x-axis

(y = 0)

3 x^{2} - 12 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 \cdot 8}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 \cdot 8 = 43

x_{1, 2} = \frac{- ( - 12 ) \pm 4 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 4 3}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - 4 3}{2 \cdot 3}

x = \frac{- ( - 12 ) + 4 3}{2 \cdot 3} : \frac{2 ( 3 + 3 )}{3}

x = \frac{- ( - 12 ) - 4 3}{2 \cdot 3} : \frac{2 ( 3 - 3 )}{3}

The solutions to the quadratic equation are:

x = \frac{2 ( 3 + 3 )}{3}, x = \frac{2 ( 3 - 3 )}{3}

3 z^{2} - 5 z - 2 = 0

2 x^{2} - 11 x + 13 = 0

470 = 1.33 x - 0.04 x^{2}

a^{2} + 10 a + 2 = 0

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

What are the solutions to the equation roots 3x^2-12x+8 ?
The solutions to the equation roots 3x^2-12x+8 are x=(2(3+sqrt(3)))/3 ,x=(2(3-sqrt(3)))/3
Find the zeros of roots 3x^2-12x+8
The zeros of roots 3x^2-12x+8 are x=(2(3+sqrt(3)))/3 ,x=(2(3-sqrt(3)))/3