Math, asked by dhruvkaushik5691, 2 days ago

find a roots of the quadritic equation, by the method of completing square method.
4x^2+4root3x +3=0

Answers

Answered by rahil5166
1

Answer:

Roots are x = -\frac{\sqrt{3}}{2}x=−

2

3

Or x = -\frac{\sqrt{3}}{2}x=−

2

3

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}x

2

+

3

x=

4

−3

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

2

+2×x×

2

3

=

4

−3

\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}⟹x

2

+2×x×

2

3

+(

2

3

)

2

=

4

−3

+(

2

3

)

2

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

⟹(x+

2

3

)

2

=

4

−3

+(

4

3

)

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

2

3

)

2

=0

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

2

3

)=0

Or

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

2

3

)=0

Therefore,

x = -\frac{\sqrt{3}}{2}x=−

2

3

Or

x = -\frac{\sqrt{3}}{2}x=−

2

3

[ Equal roots]

••••

Answered by madihasadath
2

Step-by-step explanation:

completing square method.

4x^2+4root3x +3=0

Which exam??

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