Question
Fri February 18, 2011 By: Pulakananda Bharali
 

if a+b+c=0, show that the roots of eq. ax*x+bx+c=0 are rational

Expert Reply
Wed February 23, 2011
Dear Student,
Here is the solution:
 
Since a + b + c = 0 hence b = -(c + a)

The given quadratic equation is ax2 + bx + c = 0

Or ax2 –(c + a)x + c = 0 (1)

The discriminant of equation (1) is {-(c + a)}2 – 4ac = (c + a)2 – 4ac = (c - a) 2

Since a, b, c are rational and the discriminant of equation (1) is a perfect square, hence the roots of (1) are rational. 
 
Regards
Team Topperlearning.
Home Work Help