CAT 2020 Quant Question [Slot 1] with Solution 18

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

  1. 0
  2. 40
  3. 10
  4. 20
Option: 4
Solution:

Given \(f(5 + x) = f(5 - x)\)

Put \(x = x - 5\)

\(f(x) = f(10 - x)\)

\(\therefore \) Let a, b be two roots of f(x)=0, then \(10 - a,10 - b\) are also roots of \(f(x) = 0\)

\(\therefore \) Hence sum of the roots \( = a + b + 10 - a + 10 - b = 20\)

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