Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let 
and 
and 
has 2 distinct real roots, then which of the following is true ?
A
Atleast one root must be positive
B
C
Minimum value of 
is negative
is negative D
Vertex of graph of 
lies in 3rd quadrat
lies in 3rd quadrat
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b, c)
Given 
and 
.
• Symmetry condition 
graph is symmetric about 
.
For quadratic 
:
So 
or 
• Two distinct real roots
For upward parabola with two roots:
So minimum value is negative.
Check options
Roots symmetric about 
.
Both cannot be negative ⇒ at least one root positive.
Since 
:
✓ 
Vertex 
not in 3rd quadrant. 
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