Verified Solution • 2025–26 Session moderate

QJEEM22Ma1ff7: JEE Main 2022 Mathematics - Class 11 JEEM22Ma1ff7 Solution: Let f(x) be a quadratic polynomial such that f( 2) + f(3) = 0.…

Let f(x) be a quadratic polynomial such that f( −- 2) + f(3) = 0. If one of the roots of f(x) = 0 is −- 1, then the sum of the roots of f(x) = 0 is equal to :

Multiple Choice Options

  • A 113{{11} \over 3}
  • B 73{{7} \over 3}
  • C 133{{13} \over 3}
  • D 143{{14} \over 3}

Step-by-Step Verified Solution

∵\because x = −- 1 be the roots of f(x) = 0

∴\therefore Let f(x)=A(x+1)(x−1)f(x) = A(x + 1)(x - 1) ...... (i)

Now, f(−2)+f(3)=0f( - 2) + f(3) = 0

⇒A[−1(−2−b)+4(3−b)]=0\Rightarrow A[ - 1( - 2 - b) + 4(3 - b)] = 0

b=143b = {{14} \over 3}

∴\therefore Second root of f(x) = 0 will be 143{{14} \over 3}

∴\therefore Sum of roots =143−1=113= {{14} \over 3} - 1 = {{11} \over 3}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring