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 a is (where [.],{.},sgn x represents greatest integer function , fractional part function and signum function respectively)

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

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 a is (where [.],{.},sgn x represents greatest integer function , fractional part function and signum function respectively)
Answer» Let $f (x) = ([a]^{2} - 5 [a] + 4) x^{3} + (6 {a}^{2} - 5 {a} + 1) x - (tan x) \times sgn x$ be an even function for all $x \in R,$ then the sum of all possible values of $a$ is (where $[.], {.}, sgn x$ represents greatest integer function , fractional part function and signum function respectively)