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MathsJEE Main 28 Jan 2026, Shift 2·Q7·MCQ·Moderate

Quadratic Equations · Location of roots

Let the arithmetic mean of 1a\dfrac1a and 1b\dfrac1b be 516\dfrac{5}{16}, a>2a > 2. If α\alpha is such that a,4,α,ba, 4, \alpha, b are in A.P., then the equation αx2−ax+2(α−2b)=0\alpha x^2 - ax + 2(\alpha - 2b) = 0 has :
  1. (1)One root in (1,4)(1, 4) and another in (−2,0)(-2, 0)
  2. (2)One root in (0,2)(0, 2) and another in (−4,−2)(-4, -2)
  3. (3)Complex roots of magnitude less than 2
  4. (4)Both roots in the interval (−2,0)(-2, 0)

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