CAT 2020 Functions Question (Medium)

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 the roots is

Accepted Answer

Step 1 We are given that f 5 x f 5 x for all real x This implies that the function is symmetric about x 5. So, for every root r of the function, its mirror image about x 5 i.e., 10 r is also a root. Step 2 f x 0 has four distinct real roots. By the symmetry, the roots must be in pairs that add up to

CAT 2020

Quantitative

Functions

Medium

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

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