Thank you for reporting, we will resolve it shortly
Q.
If $2 + i$ and $\sqrt{5}-2i$ are the roots of the equation $\left(x^{2}+ax+b\right)\left(x^{2}+cx+d\right)=0,$ where $a, b, c, d$ are real constants, then product of all roots of the equation is
WBJEEWBJEE 2015Complex Numbers and Quadratic Equations
Solution:
If one root of a quadratic equation is of the form $a+i b$, then other root will be $a-i b$.
So, all the roots are $2 \pm i, \sqrt{5} \pm 2 i$
$\therefore $ Product of all the roots
$=(2+i)(2-i)(\sqrt{5}+2 i)(\sqrt{5}-2 i)$
$=(4+1)(5+4)=5 \times 9=45$