Question

Factories the following :√3x^2+4x+√3​

Answer 1

Given equation

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

Solving, we get,

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

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

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

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

Now,

$\sqrt{3} x + 1 = 0$

$\implies x = \dfrac{-1}{\sqrt{3} }$

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

$\boxed{\boxed{\bold{Therefore, \ the \ factorised \ expression \ is \ (\sqrt{3}x + 1)(x+\sqrt{3}) }}}}}$

                                                             

Answer 2

Answer:

Given equation

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

3

x

2

+4x+

3

=0

Solving, we get,

\begin{lgathered}\sqrt{3} x^{2} +4x+\sqrt{3} =0\\\end{lgathered}

3

x

2

+4x+

3

=0

\implies \sqrt{3}x^{2} +3x + x + \sqrt{3} = 0⟹

3

x

2

+3x+x+

3

=0

\implies \sqrt{3}x(x+\sqrt{3})+1(x+ \sqrt{3}) = 0⟹

3

x(x+

3

)+1(x+

3

)=0

\implies (\sqrt{3}x + 1)(x+\sqrt{3}) = 0⟹(

3

x+1)(x+

3

)=0

Now,

\sqrt{3} x + 1 = 0

3

x+1=0

\implies x = \dfrac{-1}{\sqrt{3} }⟹x=

3

−1

\begin{lgathered}x+\sqrt{3}= 0\\ \implies x = -\sqrt{3}\end{lgathered}

x+

3

=0

⟹x=−

3