Question

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

• A. $\frac{5\pm \sqrt{19}}{3}$
• B. $\frac{3\pm \sqrt{19}}{5}$​
• C. $5$
• D. $3$

Answer 1

The correct option is B

$\frac{3\pm \sqrt{19}}{5}$​

Multiply the equation by 5.

we get $25x^2–30x–10=0$

$(5x{)}^2–[2\times \left(5x\right)\times 3]+3^2–3^2–10=0$
$(5x–3{)}^2–9–10=0(5x–3{)}^2–19=0(5x–3{)}^2=195x-3=\pm \sqrt{19}x=\frac{3\pm \sqrt{19}}{5}$

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