If a + b + c = 0 and a, b, c are rational, then the roots of the equation (b + c – a) x2 + (c + a – b) x + (a + b– c) = 0 are

We have,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=perfect square∴Roots are rational