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Byju's Answer
Standard X
Mathematics
Nature of Roots
For what valu...
Question
For what values of k, the equation
k
x
2
-
6
x
-
2
=
0
has real roots?
(a)
k
≤
-
9
2
(b)
k
≥
-
9
2
(c)
k
≤
-
2
(d) None of these
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Solution
(b)
k
≥
-
9
2
It is given that the roots of the equation (
k
x
2
−
6
x
−
2
=
0
)
are real.
∴
D
≥
0
⇒
(
b
2
−
4
a
c
)
≥
0
⇒
(
−
6
)
2
−
4
×
k
×
(
−
2
)
≥
0
⇒
36
+
8
k
≥
0
⇒
k
≥
−
36
8
⇒
k
≥
−
9
2
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