Question

If equation ${ax}^2+bx+c=0$ and $x^2+2x+3=0$ have a common root, then if $a:b:c=A:B:C$ then $A+B+C=$

Answer 1

Since roots $x^2+2x+3=0$ are imaginary and equation $x^2+2x+3=0$ & ${ax}^2+bx+c=0$ have common root, therefore both roots will be common.

Hence both equation are identical.
$\therefore \frac{a}{1}=\frac{b}{2}=\frac{c}{2}$ $\therefore$ $a:b:c=A:B:C$
So $A=1$, $B=2$ and $C=2$

So the sum $=6$