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Byju's Answer
Other
Quantitative Aptitude
Descartes' Rule
Product of re...
Question
Product of real roots of the equation
t
2
x
2
+
|
x
|
+
9
=
0
A
is always positive
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B
is always negative
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C
does not exist
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D
none of these
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Solution
The correct option is
C
does not exist
t
2
x
2
+
|
x
|
+
9
=
0
Now
t
2
always
≥
0
__(1)
and
t
2
x
2
always
≥
0
__(2)
|
x
|
always
≥
0
as
|
−
v
e
|
=
+
v
e
__(3)
a
>
0
__(4)
Now Adding (2), (3), (4) will always give value greater than 0 and never equal to 0.
∴
No real root exist for the given equation.
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