The number of real roots of the equation (x-1)²+(x-2)²+(x-3)² = 0 is

(a) 2

(b) 1

(c) 0

(d) 3

Please Explain.

For given equation to have real roots, D ≥ 0.

Here, D = (–12)² –4 (14) (3)

 = 144 – 168

 = –24 <0

Here D < 0, therefore the given equation have only imaginary roots.

Hence, the given equation have zero real roots.