Question

Which among the following is/are the roots of the equation
$5x^2–6x–2=0$ ?

• 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 $\frac{3\pm \sqrt{19}}{5}$​


Given, $5x^2–6x–2=0$
Multiplying the equation by 5.
We get $25x^2–30x–10=0$

Can be written as:
$(5x{)}^2–(2\left)\right(5x\left)\right(3)+3^2–3^2–10=0(5x–3{)}^2–9–10=0(5x–3{)}^2–19=0(5x–3{)}^2=195x-3=\pm \sqrt{19}x=\frac{3\pm \sqrt{19}}{5}$

$\therefore$ Roots are $\frac{3\pm \sqrt{19}}{5}$