find the roots of the following quadratic equations,if they exist 4x^2+4√3x+3
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Answer:
Step-by-step explanation:
We have 4x
2
+4
3x
+3=0
On dividing both sides by 4 we have
x
2
+
3x
+
4
3
=0
⇒ x
2
+
3x
+(
2
3
)
2
−(
2
3
)
2
+
4
3
=0
⇒ (x+
2
3
)
2
−
4
3
+
4
3
=0⇒(x+
2
3
)
2
=0....(i)
Roots exist
∴ (i) ⇒ x=−
2
3
,−
2
3
Hence the roots of given equation are −
2
3
and −
2
3
We have 4x
2
+4
3x
+3=0
On dividing both sides by 4 we have
x
2
+
3x
+
4
3
=0
⇒ x
2
+
3x
+(
2
3
)
2
−(
2
3
)
2
+
4
3
=0
⇒ (x+
2
3
)
2
−
4
3
+
4
3
=0⇒(x+
2
3
)
2
=0....(i)
Roots exist
∴ (i) ⇒ x=−
2
3
,−
2
3
Hence the roots of given equation are −
2
3
and −
2
3
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