Question

find the root of √3x+4x+√3=0​

Answer 1

Given equation

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

Solving, we get,

$\sqrt{3} x^{2} +4x+\sqrt{3}=0\\ \implies \sqrt{3}x^{2} +x+ 3x +\sqrt{x} =0\\\implies x(\sqrt{3} x +1)+\sqrt{3} (\sqrt{3} x+1)=0\\\implies (x+\sqrt{3} )(\sqrt{3} x+1)=0$

Now,

$x+\sqrt{3}=0\\ \implies \boxed{\boxed{\bold{x = \sqrt{-3} }}}}$

$\sqrt{3} x+1=0\\\implies \sqrt{3}x=-1\\ \implies \boxed{\boxed{\bold{x=\dfrac{-1}{\sqrt{3} } }}}}$

                                                     

Answer 2

Factoring the above equation ,

$\sqrt{3} {x}^{2} + 4x + \sqrt{3} = 0 \\ \\ = > \sqrt{3} {x}^{2} + 3x + x + \sqrt{3} =0 \\ \\ = > \sqrt{3} x(x + \sqrt{3} ) + 1(x + \sqrt{3} ) = 0 \\ \\ (x + \sqrt{3} )( \sqrt{3} x + 1) =0 \\ \\ x = - \sqrt{3} \: or \: \frac{ - 1}{ \sqrt{3} }$