Verified Solution • 2025–26 Session moderate

QJEEM20Ma56b5: JEE Main 2020 Mathematics - Class 11 JEEM20Ma56b5 Solution: Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0.…

Let f(x) be a quadratic polynomial such that
f(–1) + f(2) = 0. If one of the roots of f(x) = 0
is 3, then its other root lies in :

Multiple Choice Options

  • A (–3, –1)
  • B (1, 3)
  • C (–1, 0)
  • D (0, 1)

Step-by-Step Verified Solution

Let the other root is α\alpha .

∴\therefore f(x) = a(x – 3) (x – α\alpha )

f(2) = a( α\alpha – 2)

f(–1) = 4a(1 + α\alpha )

Given f(–1) + f(2) = 0

⇒\Rightarrow a( α\alpha – 2 + 4 + 4 α\alpha ) = 0

⇒\Rightarrow 5 α\alpha = -2      As a ≠\ne 0

⇒\Rightarrow α\alpha = −25-\frac{2}{5} = - 0.4

∴\therefore α\alpha ∈\in (–1, 0)

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