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Mathematics
Mathematics
Problem
1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i)
2
x
2
−
3
x
+
5
=
0
2 x^{2}-3 x+5=0
2
x
2
−
3
x
+
5
=
0
(ii)
3
x
2
−
4
3
x
+
4
=
0
3 x^{2}-4 \sqrt{3} x+4=0
3
x
2
−
4
3
x
+
4
=
0
(iii)
2
x
2
−
6
x
+
3
=
0
2 x^{2}-6 x+3=0
2
x
2
−
6
x
+
3
=
0
(i)
2
x
2
−
3
x
+
5
=
0
2 x^{2}-3 x+5=0
2
x
2
−
3
x
+
5
=
0
(ii)
3
x
2
−
4
3
x
+
4
=
0
3 x^{2}-4 \sqrt{3} x+4=0
3
x
2
−
4
3
x
+
4
=
0
(iii)
2
x
2
−
6
x
+
3
=
0
2 x^{2}-6 x+3=0
2
x
2
−
6
x
+
3
=
0
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