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Byju's Answer
Standard X
Mathematics
Nature of Roots
Find the valu...
Question
Find the values of
k
for which the given equation has real roots
5
x
2
−
k
x
+
1
=
0
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Solution
The given equation is
5
x
2
−
k
x
+
1
=
0
Here,
a
=
5
,
b
=
−
k
,
c
=
1
∴
D
=
b
2
−
4
a
c
=
(
−
k
)
2
−
4
×
5
×
1
=
k
2
−
20
The given equation will have real roots if
D
≥
0
⇒
k
2
−
20
≥
0
⇒
k
≤
−
√
20
o
r
k
≥
√
20
[
∵
x
2
−
a
2
≥
0
⇒
x
≤
−
a
o
r
x
≥
a
]
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