Let the arithmetic mean of 1/a and 1/b be 5/16, where a>2. If α i… | JEE Main 2026 Mathematics PYQ

MCQMediumJEE Main 2026 · 28 January, Shift 2Arithmetic Progression (AP)

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

A
one root in $(1,4)$ and another in $(-2,0)$
B
complex roots of magnitude less than $2$
C
both roots in the interval $(-2,0)$
D
one root in $(0,2)$ and another in $(-4,-2)$

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