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Byju's Answer
Standard X
Mathematics
Roots of Quadratic Equation
Show that the...
Question
Show that the equation
x
2
+
a
x
−
4
=
0
has real and distinct roots for all real values of
a
.
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Solution
The given equation is
x
2
+
a
x
−
4
=
0
Comparing given equation with
a
x
2
+
b
x
+
c
=
0
∴
a
=
1
,
b
=
a
,
c
=
−
4
The discriminant of the given equation is given by
D
=
b
2
−
4
a
c
=
a
2
−
4
×
−
4
=
a
2
+
16
Clearly,
D
=
a
2
+
16
>
0
for all
a
∈
R
Hence, the given equation has real and distinct roots.
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0
Similar questions
Q.
For the equation
4
x
2
+
x
+
4
x
2
+
1
+
x
2
+
1
x
2
+
x
+
1
=
31
6
Which of the following statement(s) is/are correct?
Q.
Show that the roots of the equation
x
2
+
p
x
−
q
2
=
0
are real for all real values of p and q
Q.
If
x
2
+
(
a
−
b
)
x
+
(
1
−
a
−
b
)
=
0
,
where
a
,
b
∈
R
,
the value of
a
such that the equation has distinct real roots for all value of
b
are
Q.
Show that there is no real number p for which the equation
x
2
−
3
x
+
p
=
0
has two distinct roots in [0,1].
Q.
The sum of all possible value(s) of
a
so that the equation
(
x
2
+
2
a
x
+
2
a
+
3
)
(
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+
2
a
x
+
4
a
+
5
)
=
0
has exactly three real and distinct roots is
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