Question

factorise:
$\sqrt{3x {}^{2} } + 4x + \sqrt{3}$
​

Answer 1

Given :

•Factorize :

$\rm{\sqrt{3}x^{2} +4x+\sqrt{3}}$

To Find :

•The roots of the quadratic equation=?

Solution :

$\\ \implies \sf \: \sqrt{3} {x}^{2} + 4x + \sqrt{3} = 0 \\ \\ \implies \sf \sqrt{3} {x}^{2} + x + 3x + \sqrt{3} = 0 \\ \\ \implies \sf \:x ( \sqrt{3}x + 1) + \sqrt{3} ( \sqrt{3} x + 1) = 0 \\ \\ \implies \sf \: ( \sqrt{3} x + 1)(x + \sqrt{3} ) = 0 \\ \\ \implies \boxed{ \sf{x = - \sqrt{3} \: \: and \: x = \frac{ - 1}{ \sqrt{3} } } }$

$\red \bigstar \sf \: roots \: of \: this \: equation \: are \: \boxed{ \sf{\: x = - \sqrt{3} \: \: and \: x = \frac{ - 1}{ \sqrt{3} } }}$

Additional information :

1. For finding the roots of any quadratic equation we use formula method
2. First we determinant method then we use formula method
3. the determinant formula shows the nature of the roots of given quadratic equation.

• Determinant method :

$\red\bigstar\boxed{\sf{\delta D=b^{2} -4ac}}$

• Formula method :

$\red\bigstar\boxed{\sf{x=\dfrac{-b \pm \sqrt{b^{2}-4ac}}{2a}}}$