Question
If , , where < , are the roots of the equation x^ 2 -( +3) x+3=0 such that 1 - 1 = 1 3 , then the sum of all possible values of is
JEE Main
Mathematics
Quadratic Equation
2026
JEE Main 2026 (28 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 8
- B. 6
- C. 2
- D. 4
Answer
B. 6
Step-by-step solution
+ = +3 , = 3 . 1 - 1 = - = 1 3 , so - = 3 = 1 . ( - )^2 = ( + )^2 - 4 : 1 ^2 = ( +3)^2 ^2 - 12 1 = ( +3)^2 - 12 = ^2 - 6 + 9 ^2 - 6 + 8 = 0 = 2 or = 4. Both values satisfy < (verified). Sum = 2 + 4 = 6.
Related: Mathematics — Quadratic Equation · All PYQ Banks