Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

\frac{3 \pm \sqrt{21}}{7}

\frac{7 \pm \sqrt{17}}{5}

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

None

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given equation,

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

Divide both side of equation by 5,

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

\Rightarrow x^{2} - \frac{6}{5} x - \frac{2}{5} = 0

\Rightarrow x^{2} - \frac{6}{5} x - \frac{2}{5} = 0

\Rightarrow x^{2} - 2 \times x \frac{3}{5} - \frac{2}{5} = 0

After adding and subtracting

{(\frac{3}{5})}^{2}

from left hand side, we get

\Rightarrow x^{2} - 2 \times x \times \frac{3}{5} - \frac{2}{5} + {(\frac{3}{5})}^{2} - {(\frac{3}{5})}^{2} = 0

\Rightarrow x^{2} - 2 \times x \times \frac{3}{5} + {(\frac{3}{5})}^{2} - \frac{2}{5} - {(\frac{3}{5})}^{2} = 0

\Rightarrow {(x - \frac{3}{5})}^{2} = {(\frac{3}{5})}^{2} + \frac{2}{5}

\Rightarrow {(x - \frac{3}{5})}^{2} = \frac{19}{25}

\Rightarrow x - \frac{3}{5} = \pm \sqrt{\frac{19}{25}}

\Rightarrow x - \frac{3}{5} = \pm \frac{\sqrt{19}}{5}

\Rightarrow x = \frac{3 \pm \sqrt{19}}{5}

Thus, the roots are,

x = \frac{3 + \sqrt{19}}{5}

and

x = \frac{3 - \sqrt{19}}{5}

Option 3 is Correct.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE