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

Options

  1. ANone
  2. BOnly one
  3. COnly two
  4. DThree

Correct answer

A. None

Step-by-step solution

Given that, (x-1)^2+(x-3)^2+(x-5)^2=0 aligned & x^2-2 x+1+x^2-6 x+9+x^2-10 x+25=0 & 3 x^2-18 x+35=0 aligned Discriminant D =(-18)^2-4 3 35=-96 < 0 Discriminant is negative. So, the given equation does not have any real roots.

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