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Solve $3 x^{2} + 2 x - 1 = 0$ by completing the square. The roots are:

Class 10Completing the SquareQuadratic Equations

A $\frac{1}{3}$ and -1
B $- \frac{1}{3}$ and 1
C $\frac{1}{3}$ and 1
D $- \frac{1}{3}$ and -1

Step-by-Step Solution

Divide by 3:

x^{2} + \frac{2}{3}

x - \frac{1}{3} = 0. (x + \frac{1}{3})^{2} = \frac{1}{3} + \frac{1}{9} = \frac{4}{9}, x + \frac{1}{3} = + / - \frac{2}{3}, x = \frac{1}{3}

or

x = - 1

.

Answer: A)

\frac{1}{3}

and -1

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