Question

The given quadratic equation have real roots and the roots are$-2\sqrt{3},\frac{-\sqrt{3}}{2}$ :
$2x^2+5\sqrt{3}x+6=0$

• A. True
• B. False

Answer 1

The correct option is A True

$2x^2+5\sqrt{3}x+6=0$

$\Rightarrow$ $2x^2+4\sqrt{3}x+\sqrt{3}x+6=0$

$\Rightarrow$ $2x(x+2\sqrt{3})+\sqrt{3}(x+2\sqrt{3})=0$

$\Rightarrow$ $(x+2\sqrt{3})(2x+\sqrt{3})=0$

$\Rightarrow$ $x+2\sqrt{3}=0$ and $2x+\sqrt{3}=0$

$\therefore$ $x=-2\sqrt{3}$ and $x=\frac{-\sqrt{3}}{2}$

$\therefore$ We can see, roots given in question are correct.