Question

Given that the equation $z^2+(p+iq)z+r+is=0$where p,q,r,s are real and non-zero has a real root, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given that $z^2+(p+iq)z+r+is=0$......(i)
Let z= $\alpha$ (where $\alpha$ is real) be a root of (i), then
${\alpha }^2+(p+iq)\alpha +r+is=0Or{\alpha }^2+p\alpha +r+i(q\alpha +s)=0$
Equating real and imaginary parts, we have ${\alpha }^2+p\alpha +r=0$ and $q\alpha +s=0$
Eliminating we get ${\left(\frac{-s}{q}\right)}^2+p\left(\frac{-s}{q}\right)+r=0$
or $s^2-pqs+q^{2}4=0$ or $pqs=s^2+q^{2}r$