Concept of roots in Quadratic Equation $a$ , $b$, $c$ are real numbers where a is not equal to zero and the quadratic equation 
\begin{align} 
ax^2 + bx +c =0   
\end{align} 
has no real roots then prove that $c(a+ b+ c)>0$  and  $a(a+ b + c) >0$ 
My Approach : As the equation has no real roots then its discriminant is less than zero.  So the graph of the equation will be above  $x$-axis or below $x$-axis . 
I am able to conclude signs of $a$ , $b$, $c$ but still not getting appropriate answer. 
Please explain the concept......

For the second part, another justification is that since the discriminant is less than zero, then it must hold that $a,c$ have the same sign. Why? If $a,c$ had opposite signs then the discriminant $\Delta = b^2-4ac$ would have been positive.
Since $c,(a+b+c)$ have the same sign and $c,a$ have the same sign then $a,(a+b+c)$ have the same sign as well, thus:
$$a(a+b+c) >0.$$
