Let ' 
' be a real number. The minimum number of distinct real roots possible of the equation 
is :
Text Solution
Verified by ExpertsB
Step 1: Analyze each quadratic
Discriminant: 
real roots exist if 
or 
If 
no real root
Discriminant: 
always 
always 2 real roots
Step 2: Minimum number of distinct roots
For 
, first quadratic has 0 real roots, second has 2 real roots → total 2 distinct roots
For 
, first quadratic has 2 roots, second always has 
total 4 roots
Hence, the minimum number of distinct real roots occurs when 
roots
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems