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

Asked by pulakananda | 18th Feb, 2011, 09:29: PM

Expert Answer:

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.

Answered by  | 23rd Feb, 2011, 07:23: PM

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