Question

If a, b, c are the roots of the equation x3 – 6x2 + 11x – 6 = 0, then find the centroid of the triangle whose vertices are (ab, 1/ab), (bc, 1/bc), (ca, 1/ca).

Answer 1

By hypothesis

a + b + c = 6

ab + bc + ca= 11

and abc = 6

Therefore

ab + bc + ca /3 = 11/3

and

1/3 (1/ab + 1/bc + 1/ca) = a + b + c/2abc = 6/3 x 6 = 1/3

Hence, the centroid of the triangle is

Caution: First, we have to check whether a, b, c are real or not. In the present case, the roots of the given equation are 1, 2 and 3.