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Byju's Answer
Standard XI
Mathematics
Nature of Roots
If ax2+2bx+ 3...
Question
If
a
x
2
+
2
b
x
+
3
c
=
0
,
a
ā
0
,
c
>
0
does not have any real roots, then which of the following is/are true?
A
4
a
−
4
b
+
3
c
>
0
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B
a
+
6
b
+
27
c
>
0
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C
4
a
−
4
b
+
3
c
<
0
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D
a
+
6
b
+
27
c
<
0
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Solution
The correct option is
B
a
+
6
b
+
27
c
>
0
Let
f
(
x
)
=
a
x
2
+
2
b
x
+
3
c
Now,
f
(
x
)
=
0
does not have real root,
Checking
f
(
0
)
=
3
c
>
0
, so
f
(
x
)
>
0
∀
x
∈
R
Now,
f
(
−
2
)
>
0
⇒
4
a
−
4
b
+
3
c
>
0
f
(
1
3
)
>
0
⇒
a
9
+
2
b
3
+
3
c
>
0
⇒
a
+
6
b
+
27
c
>
0
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1
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