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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 following equations have real roots.
x
2
−
4
k
x
+
k
=
0
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Solution
x
2
−
4
k
x
+
k
=
0
This is in the form of
a
x
2
+
b
x
+
c
=
0
Here
a
=
1
,
b
=
−
4
k
,
c
=
k
For the equation to have real roots ,
discriminant
≥
0
⟹
(
−
4
k
)
2
−
4
(
1
)
(
k
)
≥
0
⟹
k
(
4
k
−
1
)
≥
0
⟹
k
∈
(
−
∞
,
0
]
∪
[
1
/
4
,
∞
)
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