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Question

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

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is D 0
(x1)2+(x2)2+.............+(xn)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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