The number of real root of the equation $(x - 1)^{2} + (x - 2)^{2} + (x - 3)^{2} + (x - 4)^{2} + . . . . . + (x - n)^{2} = 0$

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Solution

The correct option is D $0$
$(x - 1)^{2} + (x - 2)^{2} + . . . . . . . . . . . . . + (x - n)^{2} = 0$
clearly this is a quadratic equation equation equation since all the terms are quadratic.
Now, we know square of any term is always non-negative .
Therefore,
This equation will never cross x-axis that is it will always be greater than zero.
The parabola graphically will never cross x-axis and hence there will be no real solution.
Hence, the answer zero.

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The number of real root of the equation (x−1)2+(x−2)2+(x−3)2+(x−4)2+.....+(x−n)2=0

The number of real root of the equation $(x - 1)^{2} + (x - 2)^{2} + (x - 3)^{2} + (x - 4)^{2} + . . . . . + (x - n)^{2} = 0$