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Byju's Answer
Standard X
Mathematics
Formation of a Quadratic Equation From It's Roots
If the roots ...
Question
If the roots of the equation
x
2
−
8
x
+
a
2
−
6
a
=
0
are real and distinct then find number of all possible integral values of
a
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Solution
Since the roots of the given equation are real and distinct, we must have
D
>
0
⇒
64
−
4
(
a
2
−
6
a
)
>
0
⇒
4
[
16
−
a
2
+
6
a
]
>
0
−
4
(
a
2
−
6
a
−
16
)
>
0
⇒
a
2
−
6
a
−
16
<
0
⇒
(
a
−
8
)
(
a
+
2
)
<
0
⇒
−
2
<
a
<
8
Hence, the roots of the given equation are real if '
a
' lies between
−
2
and
8
.
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