Explanation

(a)
Given equation can be rewritten as
$3x^{2} - (a + c + 2b + 2d)x + ac + 2bd = 0$
$\therefore\$Discriminant, $D$
$= (a + c + 2b + 2d)^{2} - 4 \bullet 3(ac + 2bd)$
$= \left\{ (a + 2d) + (c + 2b) \right\}^{2} - 12(ac + 2bd)$
$= \left\{ (a + 2d) + (c + 2b) \right\}^{2} + 4(a + 2d)(c + 2b) - 12(ac + 2bd)$
$= \left\{ (a + 2d) + (c + 2b) \right\}^{2} - 8ac + 8ab - 8dc - 8bd$
$= \left\{ (a + 2d) + (c + 2b) \right\}^{2} + 8(c - b)(d - a)$
Which is$+ ve$, since $a < b < c < d$.
Hence, roots are real and distinct.