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Find the roots of the quadratic equation 4x^2 + 4√3x + 3 = 0 - Mathematics

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Sum

Find the roots of the quadratic equation 4x2 + 4√3x + 3 = 0

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Solution

4x2 + 4√3x + 3 = 0

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

`"i.e "x^2+2xxxxxsqrt3/2+(sqrt3/2)^2-(sqrt3/2)^2+3/4=0`

`=>( x+\frac{\sqrt{3}}{2})^2 -\frac{3}{4}+\frac{3}{4}=0`

`"i.e."(x+sqrt3/2)^2=0`

`\Rightarrow x+\frac{\sqrt{3}}{2}=0\text{ and }x=\frac{-\sqrt{3}}{2}`

Concept: Solutions of Quadratic Equations by Completing the Square
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