Quantitative Aptitude – Progression – If f(5+x) = f(5-x) for every real x


Slot – 1 – Quantitative Aptitude – Progression – If f(5+x) = f(5-x) for every real x


Q. 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. 40
  2. 10
  3. 20
  4. 0

Answer: 20

Solutions:
Given,
f(5-x) = f(5+x)
Put (5 +x) = k or -x = 5 –k
So f(5 +5 -k ) = f(k)
F(10-k) = f(k)
From this we can say if (k) = 0 then f(10-k) =0
Or if k is one root then 10-k will be other root and if x is 3rd root the 10-x will be fourth root thus sum of roots = k + 10-k + x+10-x = 20


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