Question

if a, b, c are integers, P.T. roots of equation (b - c) x² + (c - a) x + (a - b) = 0 are rational​

Answer 1

Answer:

Yes it is rational

Step-by-step explanation:

We have, (b+c−a)x2+(c+a−b)x+(a+b−c)=0

D=(c+a−b)2−4(b+c−a)(a+b−c)=(a+b+c−2b)2−4(a+b+c−2a)(a+b+c−2c)=(−2b)2−4(−2a)(−2c)=4(b2−4ac)=4((−a−c)2−4ac)=4(a−c)2=(2(a−c))2

which is a perfect square.

Hence roots are rational.