For what value of a, quadratic equation 3ax²- 6x +1=0 has no real roots *
1 point
a < 3
a=3
a > 3
a ‡3
Answers
Answered by
0
Answer:
3 Answers
Ratnaker Mehta
May 8, 2018
−
1
<
p
<
−
1
9
,
or
,
p
∈
(
−
1
,
−
1
9
)
.
Explanation:
We know that, the quadr. eqn.,
a
x
2
+
b
x
+
c
=
0
will have no real roots
⇔
b
2
−
4
a
c
<
0
.
Therefore, in our case, we must have,
(
3
p
+
1
)
2
−
4
⋅
1
⋅
(
−
p
)
<
0
.
∴
9
p
2
+
6
p
+
1
+
4
p
<
0
,
i
.
e
.
,
9
p
2
+
10
p
+
1
<
0
.
∴
(
p
+
1
)
(
9
p
+
1
)
<
0
.
∴
Case
(
1
)
:
(
p
+
1
)
<
0
and
(
9
p
+
1
)
>
0
,
or
,
Case
(
2
)
:
(
p
+
1
)
>
0
,
and
(
9
p
+
1
)
<
0
.
Case (1) :
(
p
+
1
)
<
0
and
(
9
p
+
1
)
>
0
.
∴
p
<
−
1
and
p
>
−
1
9
. This is impossible.
Similarly, in Case (2) , we have,
p
>
−
1
,
&
,
p
<
−
1
9
,
or
,
−
1
<
p
<
−
1
9
.
We conclude that,
p
∈
(
−
1
,
−
1
9
)
.
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Answered by
5
Answer:
a > 3
Step-by-step explanation:
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