sum: m + n = -b/a
product: mn = c/a
substitute. when proving, you only manipulate/solve one side.
mnb^2=(m+n)^2 ac
(c/a)(b^2) =? (ac)(m+n)^2
(c/a)[a(m + n)]^2 =? (ac)(m+n)^2
(c/a)(a^2)(m+n)^2 =? (ac)(m+n)^2
(ac)(m+n)^2 = (ac)(m+n)^2
this problem is pretty much the same as the one you posted earlier. you should also check Naruto's answer on that post.
If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m:n
prove that mnb^2=(m+n)^2 ac
2 answers
Gee! Naruto and Sasuke seem to be the same person!!