What are the solutions to the equation roots 3x^2-2x-1 ?

The solutions to the equation roots 3x^2-2x-1 are x=1,x=-1/3

Find the zeros of roots 3x^2-2x-1

The zeros of roots 3x^2-2x-1 are x=1,x=-1/3

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roots

3 x^{2} - 2 x - 1

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

Solution steps

3 x^{2} - 2 x - 1

The roots are the intercepts with the x-axis

(y = 0)

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

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 3 (- 1) = 4

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

Separate the solutions

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

x = \frac{- ( - 2 ) + 4}{2 \cdot 3} : 1

x = \frac{- ( - 2 ) - 4}{2 \cdot 3} : - \frac{1}{3}

The solutions to the quadratic equation are:

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

(x + 5)^{2} = 2 (x + 9)

x^{2} - 3 x - 10 = 0

\frac{1}{8} x^{2} = x + 16

0 = 9 x^{2} + 6 x + 1

x, x^{2} - 5 x + 6 = x + 3

What are the solutions to the equation roots 3x^2-2x-1 ?
The solutions to the equation roots 3x^2-2x-1 are x=1,x=-1/3
Find the zeros of roots 3x^2-2x-1
The zeros of roots 3x^2-2x-1 are x=1,x=-1/3