If f(5 + x) = f(5 &ndash; x) for every real x, and f (x) = 0 has four distinct real roots, then the sum of these&nbsp;roots is&nbsp;

CAT 2020 Question Paper | CAT Verbal Ability Slot 1

Question :

If f(5 + x) = f(5 – x) for every real x, and f (x) = 0 has four distinct real roots, then the sum of these roots is

Started 3 months ago by Shashank in

A.
20
B.
40
C.
10
D.
0

Option A is the correct answer.

Explanatory Answer

As f(x) = 0 we must try to convert f(5+x) = f(5-x) in terms of f(x)
We substitute x as x-5
f(x) = f(10-x)
Lets assume x = A as a root, then we simultaneously get 10-A as a root
Similarly we assume x = B as a root, then we get 10-B as a root
the 4 roots are A, B, 10-A, 10-B
The sum of roots is 20