factorise by completing square 4x^2 + 4√3x + 3
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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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