Question
Let a, b C . Let , be the roots of the equation x^2 + ax + b = 0. If - = 11 and ^2 - ^2 = 3i 11 , then ( ^3 - ^3)^2 is equal to:
JEE Main
Mathematics
Quadratic Equation
2026
JEE Main 2026 (05 April Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 160
- B. 176
- C. 194
- D. 187
Answer
B. 176
Step-by-step solution
Given - = 11 and ^2 - ^2 = 3i 11 + = ^2 - ^2 - = 3i 11 11 = 3i Using the identity ( - )^2 = ( + )^2 - 4 ( 11 )^2 = (3i)^2 - 4 11 = -9 - 4 4 = -20 = -5 Now, ^3 - ^3 = ( - )( ^2 + + ^2) ^3 - ^3 = ( - )(( + )^2 - ) ^3 - ^3 = 11 ((3i)^2 - (-5)) ^3 - ^3 = 11 (-9 + 5) = -4 11 Squaring both sides, we get: ( ^3 - ^3)^2 = (-4 11 )^2 = 16 11 = 176 Answer: 176
Related: Mathematics — Quadratic Equation · All PYQ Banks