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Question 220027
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Both real roots between 0 and 1 MCQ

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Both real roots between 0 and 1HardQuestion 220027

Question

For both roots of x² − bx + c = 0 to lie in (0, 1), necessary conditions include:
  1. A
    b < 2, c < 1, b² > 4c, 0 < b and 0 < c
  2. B
    b > 0, c > 0, D ≥ 0, f(0)>0, f(1)>0
    Correct
  3. C
    b > 2, c < 1
  4. D
    b < 0, c > 0

Correct answer

b > 0, c > 0, D ≥ 0, f(0)>0, f(1)>0

Explanation

For both roots in (0,1): D ≥ 0 (real roots), f(0) = c > 0, f(1) = 1−b+c > 0, and 0 < vertex = b/2 < 1.

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