Explanation

(b)
$\because a^{- 1},\ b^{- 1},\ c^{- 1}$ are in AP
$\therefore a,\ b,\ c$ are in HP.
Now, for numbers $a^{101},b^{101},c^{101}$
$AM > GM$
$\Rightarrow \ \frac{a^{101} + c^{101}}{2} > \left( \sqrt{ac} \right)^{101} > b^{101}\ \ \ \ \ (\because\ \sqrt{ac} > b)$
$\Rightarrow 2b^{101} - a^{101} - c^{101} < 0$ …(i)
Now, product of roots of given equation
$= \frac{2b^{101} - a^{101} - c^{101}}{1} < 0$ [from relation (i)]