Question

Show that the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are RATIONAL

Answer 1

simply find the discriminant of the equation..

Answer 2

ok

Answer 3

well u just need to show that Discriminant of this quadratic is a perfect square

Answer 4

and as well discriminant has to be aperfect sqaure

Answer 5

and u should mention that \(a\) , \(b\) and \(c\) are rational numbers

Answer 6

\[a(b-c)x^2+b(c-a)x+c(a-b)=0\]\[\Delta=b^2(c-a)^2-4a(b-c)c(a-b)\]\[\Delta=b^2c^2+b^2a^2-2acb^2-4ac(-b^2+bc+ba-ca)\]\[\Delta=b^2c^2+b^2a^2-2acb^2+4acb^2-4abc^2-4bca^2+4a^2c^2\]\[\Delta=b^2c^2+b^2a^2+4a^2c^2+2acb^2-4abc^2-4bca^2\]\[\Delta=(bc+ba-2ac)^2\]

Answer 7

\[x=\frac{b(a-c)\pm|bc+ba-2ac|}{2a(b-c)}\]is rational