ii) 4x2 + 43x + 3 = 0
Answers
Answer:
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]
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