Find the roots of the equation 5x2–6x–2=0 by the method of complet

Question

Find the roots of the equation

5 x^{2} - 6 x - 2 = 0

by the method of completing the square.

Options:

A . 5±√193

B . 3±√195

C . 5

D . 3

Answer: Option B
:
B
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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