If two equations ` x^(2) + ax + bc = 0 and x^(2) + bx + ca =0` have a common root, the find the condition and the quadratic with other roots of the equations.

Options

A. a = b
B. a + b = -1
C. a + b = 1
D. a - b = 1

Answer

D

Explanation

Let `lambda` be the common root of the given equations. Then, `lambda^(2) - a lambda + b = 0 and lambda^(2) + b lambda - a = 0`
On subtraction, we get `lambda^(2)(a+b) - (a+b) = 0 rArr a + b = 0 or, lambda = 1`
Putting `lambda = 1 "in" lambda^(2) - a lambda + b = 0`, we ge `1 - a + b = 0 rArr a - b = 1`.