Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square.

$\frac{5 \pm \sqrt{19}}{3}$

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$\frac{3 \pm \sqrt{19}}{5}$

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$5$

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$3$

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Solution

The correct option is B
$\frac{3 \pm \sqrt{19}}{5}$

Multiply the equation by 5.

we get $25 x^{2} - 30 x - 10 = 0$

$(5 x)^{2} - [2 \times (5 x) \times 3] + 3^{2} - 3^{2} - 10 = 0$
$(5 x - 3)^{2} - 9 - 10 = 0 (5 x - 3)^{2} - 19 = 0 (5 x - 3)^{2} = 19 5 x - 3 = \pm \sqrt{19} x = \frac{3 \pm \sqrt{19}}{5}$

Roots of the equation are $\frac{3 + \sqrt{19}}{5} & \frac{3 - \sqrt{19}}{5}$

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