Question

If the sum of the squares of the roots of the quadratic equation ax^2 + bx + c = 0 is m:n, prove that b^2= 2ac + 4a^2

I really have no idea how to prove it so pls help

Answer 1

one root: [-b+sqrt(b^2-4ac)]/2a
squared: b^2 -2bsqrt(b^2-4ac) + b^2-4ac]/4a^2


second root : [-b-sqrt(b^2-4ac)]/2a
squared: b^2 +2bsqrt(b^2-4ac) + b^2-4ac]/4a^2

sum: [ 4 b^2 - 8ac ] / 4a^2

= [b^2 -2ac]/a^2
now I have no idea what m:n means so you have to take it from there.