Functions

by logic, i am getting a,b,d .

@vivek f(4-x)=-f(4+x) otherwize it will become many to one.

I am getting all a,b,c,d.
for (c)
we know f(x) passes through (4,0) and is either increasing or decreasing.
but f(-100)>0.therefore it is decreasing and f'(x)<0 always.
Now, for roots to be non real,
f'(10)²+4f'(x)<0
which may be possible as f'(10)<0.

And how do you get a,b,d?

first of all, you are slightly mistaken.

the question says that the function is symmetric about the point (4,0) and not the line x=4 .

and it should be a,b,c,d

https://www.youtube.com/watch?v=CSjzlrL5hKA