Question

4x^2+4root3x+3 = 0 find by completing the square method

Answer 1

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Answer 2

Answer:

Roots are $x = -\frac{\sqrt{3}}{2}$ Or $x = -\frac{\sqrt{3}}{2}$

Explanation:

Given Quadratic equation:

4x²+4√3x+3 = 0

=> 4x²+4√3x = -3

Divide each term by 4 , we get

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

$\implies x^{2}+2\times x\times \frac{\sqrt{3}}{2}=\frac{-3}{4}$

$\implies x^{2}+2\times x\times \frac{\sqrt{3}}{2}+\left(\frac{\sqrt{3}}{2}\right)^{2}=\frac{-3}{4}+\left(\frac{\sqrt{3}}{2}\right)^{2}$

$\implies\left(x+\frac{\sqrt{3}}{2}\right)^{2}\\=\frac{-3}{4}+\left(\frac{3}{4}\right)$

$\implies\left(x+\frac{\sqrt{3}}{2}\right)^{2}=0$

$\implies\left(x+\frac{\sqrt{3}}{2}\right)=0$

Or

$\implies\left(x+\frac{\sqrt{3}}{2}\right)=0$

Therefore,

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

Or

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

[ Equal roots]

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