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Byju's Answer
Standard XIII
Mathematics
Discriminant of a Quadratic Equation
If a,b∈1,2,3 ...
Question
If
a
,
b
∈
{
1
,
2
,
3
}
and the equation
a
x
2
+
b
x
+
1
=
0
has real roots, then
A
a
≤
b
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B
a
>
b
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C
number of possible ordered pairs
(
a
,
b
)
is
3
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D
a
<
b
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Solution
The correct option is
D
a
<
b
a
x
2
+
b
x
+
1
=
0
For real roots,
D
≥
0
b
2
−
4
a
≥
0
⇒
b
2
≥
4
a
Possible pairs of
(
a
,
b
)
are
(
1
,
2
)
,
(
1
,
3
)
,
(
2
,
3
)
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0
Similar questions
Q.
If
a
,
b
∈
{
1
,
2
,
3
}
and the equation
a
x
2
+
b
x
+
1
=
0
has real roots, then
Q.
If
a
,
b
,
c
∈
R
and the quadratic equation
a
x
2
+
b
x
+
c
=
0
has no real roots, then
Q.
For the equation
a
x
2
+
b
x
+
c
=
0
,
a
,
b
and
c
are real,
Statement 1: If the equation
a
x
2
+
b
x
+
c
=
0
,
0
<
a
<
b
<
c
, has non-real complex roots
z
1
and
z
2
, then
|
z
1
|
>
1
,
|
z
2
|
>
1
.
Statement 2: Complex roots always occur in conjugate pairs.
Q.
If the equation
a
x
2
+
b
x
+
c
=
0
has non-real roots,prove that
1
+
c
a
+
b
a
>
0
Q.
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and −ax
2
+ bx + c = 0 has real roots.
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