If the Quadratic equation αx2 + βx + a2 + b2 + c2 – ab – bc – ca = 0 has imaginary roots, then

Prove that

2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0

2. Just to clear things up, do you mean:

$ax^2+\beta x+a^2+b^2+c^2-ab-bc-ac=0$

Prove that:

$2(a-\beta)+(a-b)^2+(b-c)^2+(c-a)^2<0$?

Next time you want to show powers use the '^' symbol. e.g $2^n$ is 2^n.

If the Quadratic equation αx2 + βx + a2 + b2 + c2 – ab – bc – ca = 0 has imaginary roots, then

Prove that

2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0
The descriminant has to be negative.

RonL