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Byju's Answer
Standard VIII
Mathematics
Random Interesting Patterns Followed by Square Numbers
If ax2+bx+c...
Question
If
a
x
2
+
b
x
+
c
is a perfect square, then
b
2
=
A
2ac
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B
ac
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C
4ac
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D
√
2
a
c
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Solution
The correct option is
C
4ac
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0
Similar questions
Q.
If
a
,
b
,
c
are real and
b
2
−
4
a
c
is perfect square then the roots of the equation
a
x
2
+
b
x
+
c
=
0
, will be:
Q.
If
s
i
n
θ
and
c
o
s
θ
are the roots of
a
x
2
+
b
x
+
c
=
0
,
then
c
o
s
−
1
(
a
2
−
b
2
+
2
a
c
)
=
Q.
If sin θ and cos θ are the roots of the equation ax
2
– bx + c = 0, then a, b and c satisfy the relation
(a) a
2
+ b
2
+ 2ac = 0
(b) a
2
– b
2
+ 2ac = 0
(c) a
2
+ c
2
+ 2ab = 0
(d) a
2
– b
2
– 2ac = 0
Q.
If sin α and cos α are the roots of the equation
a
x
2
+
b
x
+
c
=
0
,
then
Q.
E
1
:
a
+
b
+
c
=
0
, if
1
is a root of
a
x
2
+
b
x
+
c
=
0
.
E
2
:
b
2
−
a
2
=
2
a
c
, if
sin
θ
and
cos
θ
are the roots of
a
x
2
+
b
x
+
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=
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.
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