Let `x_(1)` and `x_(2)` are the roots of `ax^(2)+bx+c=0 (a,b,c epsilon R) and x_(1).x_(2)lt0, x_(1)+x_(2)` is non zero, then the roots of `x_(1)(x-x_(2))^(2)+x_(2)(x-x_(1))^(2)= 0` are

Options

A. negative
B. real and opposite in sign
C. positive
D. non real

Answer

B

Explanation

Let `x_(1)` and `x_(2)` …………….
`x_(1)(x-x_(2))^(2)+x_(2)(x-x_(1))^(2)=0`
`implies x^(2)(x_(1)+x_(2))-4xx_(1)x_(2)+x_(1)x_(2)(x_(1)+x_(2))=0`
`D = 16(x_(1)x_(2))^(2)-4x_(1)x_(2).(x_(1)+x_(2))^(2)gt 0 as x_(1)x_(2)lt 0`
Product of roots `= x_(1)x_(2)lt 0`
Thus root are real of opposite signs.