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

Direction : Consider the following for the items that follow :  

The roots of the quadratic equation 

a²(b² - c²)x² + b²(c² - a²)x + c²(a² - b²) = 0 are equal (a² ≠ b² ≠ c²).

Which one of the following statements is correct? 

Direction : Consider the following for the items that follow :  

The roots of the quadratic equation 

a²(b² - c²)x² + b²(c² - a²)x + c²(a² - b²) = 0 are equal (a² ≠ b² ≠ c²).

Which one of the following is a root of the equation? 

lf f(x) = [x]² - 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions?