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NDA 2 2024 Maths, question 39

Topic: Algebra

Q39

What is the number of real roots of the equation (x−1)2+(x−3)2+(x−5)2=0(x-1)^{2}+(x-3)^{2}+(x-5)^{2}=0?

  1. (a) NoneCorrect answer
  2. (b) Only one
  3. (c) Only two
  4. (d) Three

Solution.

Answer: (a) None

  1. All three squares are nonnegative.
  2. Their sum can be zero only if x is simultaneously 1,3 and 5, which is impossible.
  3. Alternatively the sum is 3(x−3)²+8>0.
  4. There are no real roots.