Question

All the three roots of ${az}^3+{bz}^3+cz+d=0$ have negative real parts $(a,b,c\in R)$, then

• A. $ab>0$
• B. $bc>0$
• C. $ad>0$
• D. $Allofthese$

Answer 1

The correct option is A $ab>0$

The problem is negative find the condition that all roots of ,$f\left(z\right)=a{z}^3+b{z}^2+cz+d=0$

$f\text{'}\left(z\right)=3a{z}^2+2bz+c$

$z=\frac{-2b\pm -\sqrt{({4b}^2-12ac)}}{6a}$

Therefore,$\frac{-2b}{6a}<0$

$ab>0$.