If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are Answers: A) rational B) irrational C) non real D) real E) none of these.
Sol.(a) The sum of coefficients   = (b + c - a) + (c + a - b) + (a + b - c) = a + b + c = 0 (given)   ∴ x = 1 is a root of the equation   ∴ The other root is a+b−cb+c−aa+b−cb+c−a , which is rational as a,b, c, are rational   Hence, both the roots are rational.   ALTERNATIVE :   D = (c + a - b)2 - 4(b + c - a)(a + b - c)   = (-2b)2 - 4(-2a)(-2c) = 4b2 - 16ac   = 4(a + c)2 - 16ac = 4[(a + c)2 - 4ac] = 2[(a - c)2]   D is a perfect square. Hence, the roots of the equation are rational.   rationalnswer rational
<result>A</result>
If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are