Question

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

• A. $\frac{3\sqrt{3}\pm \sqrt{3}}{2}$
• B. $\frac{-3\sqrt{3}\pm \sqrt{3}}{2}$
• C. $\frac{3\pm 1}{2}$
• D. $\frac{-3\pm 1}{2}$
  

Answer 1

The correct option is B $\frac{-3\sqrt{3}\pm \sqrt{3}}{2}$

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

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

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

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

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

$x=-2\sqrt{3}$ or $x=-\sqrt{3}$

also it can be written as

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

or

$x=-\sqrt{3}=\frac{-3\sqrt{3}+\sqrt{3}}{2}$