Question

If the roots of the equation `(x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0` are equal then
A. a + b + c = 0
B. `a + b omega + c omega^(2) = 0`
C. a - b + c = 0
D. none of these

Answer 1

Correct Answer - B
The given equation can be written as `3x^(2) - 2 (a + b +c) x + (ab + bc + ca) = 0`
The roots of the equation will be equal if `4(a + b + c)^(2) - 12(ab + bc + ca) = 0`
`rArr" "a^(2)+b^(2)+c^(2) -ab-bc-ca = 0`
`rArr" "(a + b omega + c omega^(2))(a + b omega^(2)+c omega)=0`
`rArr" "a + b omega + c omega^(2) = 0 or, a + b omega^(2) + c omega = 0`