See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

Given g(x) = g(8 – x)  g(x) is symmetric about x = 4     g x g 8 x      g(4) = 0,       g 0 g 8 ; g 2 g 6 ; g 5 g 3          ;   g 7 g 1          g 0 g 1 g 2 g 3 g 4              g 5 g 6 g 7 g 8         = 0 Hence g(x) = 0 has min 9 roots in [0, 8] Now using rolle’s then  g x 0   having at least 8 roots in [0, 8] Now given equation    2 g x g x g x 0        min 9 min 8 d g x g x 0 dx    according to rolles theorem min roots of equation is 16.