2014/075) if $ax^2+bx+c = 0 $ has no real roots and $a+b+c \lt 0$ then show that $c \lt 0$

let
$f(x) = ax^2 + bx +c = 0$
if f(x) has no real root then f(x) is positive for all x or it is -ve for all x

$f(1) = a + b+ c \lt 0$

hence $f(0) = c \lt 0$