Let f(x)=([a]2−5[a]+4)x3−(6{a}2−5{a}+1)x−(tanx)×sgn x be an even function for all x∈R, then the sum of all possible values of ′3a′ is (where, [.] and {.} denote the greatest integer function and fractional part functions, respectively)

Let f(x)=([a]2−5[a]+4)x3−(6{a}2−5{a}+1)x−(tanx)×sgn x be an e

1.	Let f(x)=([a]2−5[a]+4)x3−(6{a}2−5{a}+1)x−(tanx)×sgn x be an even function for all x∈R, then the sum of all possible values of ′3a′ is (where, [.] and {.} denote the greatest integer function and fractional part functions, respectively)
Answer» Let $f (x) = ([a]^{2} - 5 [a] + 4) x^{3} - (6 {a}^{2} - 5 {a} + 1) x - (tan x) \times s g n x$ be an even function for all $x \in R$ , then the sum of all possible values of $^{'} 3 a^{'}$ is (where, [.] and {.} denote the greatest integer function and fractional part functions, respectively)