Write the number of real roots of the equation $(x - 1)^{2} + (x - 2)^{2} + (x - 3)^{2} = 0$

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Solution

$(x - 1)^{2} + (x - 2)^{2} + (x - 3)^{2} = 0 \Rightarrow x^{2} - 2 x + 1 + x^{2} - 4 x + 4 + x^{2} - 6 x + 9 = 0 \Rightarrow 3 x^{2} - 12 x + 14 = 0 N o w, D = b^{2} - 4 a c = (- 12)^{2} - 4.3.14 - 144 - 168 = - 24 < 0 ∵ D < 0 so, no real roots$

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