Which of the following is always  true

One root of the equation $a{x}^2+bx+c=0,(a,b,c\in R\&a\ne 0)$ in the form of  $p+\sqrt{q}$ then other root is  $p-\sqrt{q}$

Exactly one of the root of the equation  $a{x}^2+bx+c=0,(a\ne 0)$ lies in the given interval $(k_1,k_2)$  if  $f\left(k_1\right).f\left(k_2\right)>0$

If $a,b,c,d,e,f$  are positive real numbers and $df-e^2>0$ . 
The equations  $a{x}^2+2bx+c=0 \left(a\ne 0\right)$ and 
$d{x}^2+2ex+f=0 \left(d\ne 0\right)$  have a common root, 
then $\frac{d}{a}=\frac{e}{b}=\frac{f}{c}$

Equation $(a{x}^2+bx+c)(a{x}^2-dx-c)=0,(ac\ne 0)$  has no real roots,