Question

find the roots of the following quadratic equations if they exist by the method of completing the square 4x²+4✓3x+3=0

Answer 1

4x^2 +4√3+3 = 0
(2x+√3)(2x+√3)=0
2x+√3 = 0
x = -√3/ 2

Answer 2

$4x²+4 \sqrt{3x} + 3 = 0$

We know ;

D$= b² - 4ac$

$= (4 \sqrt{3})²- 4 \times 4 \times 3$

$= 48 - 48$

$= 0$

Since D = 0 , roots are possible for this equation .

$\implies (2x)² + 2 \times 2x \times \sqrt3 + (\sqrt {3})² = 0$

$\implies (2x + \sqrt {3})² = 0$

$\implies (2x + \sqrt 3) = 0$ and $(2x + \sqrt 3) = 0$

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