Find the roots of the following quadratic equation (if they exist ) by the method of completing the square.
$4 x^{2} + 4 \sqrt{3} x + 3 = 0$

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Solution

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

The standard quadratic equation is $a x^{2} + b x + c = 0$

$D = b^{2} - 4 a c = 48 - 4 (4) (3) = 0$

Therefore, the roots exist and are real and equal.

Equation can be rewritten as

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

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

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

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Similar questions

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

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$4 x^{2} + 4 \sqrt{3} x + 3 = 0$

2 x^{2} - 7 x + 3 = 0

2 x^{2} + x - 4 = 0

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

2 x^{2} + x + 4 = 0

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

\frac{- \sqrt{3}}{2}, \frac{- \sqrt{3}}{2}

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

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