Let the arithmetic mean of \frac{1}{a} and \frac{1}{b} be \frac{5}{16}, a>2. If \alpha is such that a, 4, \alpha, b are in A.P., then the equation \alpha x^2-a x+2(\alpha-2 b)=0 has : [28 Jan 2026 Shift 2]

Correct Answer is : one root in ( 1,4 ) and another in ( −2,0 )

one root in ( 1,4 ) and another in ( -2,0 )

one root in ( 0,2 ) and another in ( -4,-2 )

both roots in the interval (-2,0)

complex roots of magnitude less than 2

Sequences and Series Part 3

Section: Mathematics

Question : 2 of 93

Marks: +1, -0

Let the arithmetic mean of ‌

and ‌

be ‌

,a>2. If α is such that a,4,α,b are in A.P., then the equation αx2−ax+2(α−2b)=0 has :

[28 Jan 2026 Shift 2]

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