Question

Quadratic equation $x^2+(a-1)ix+5=0(a\in R)$ will have a pair of conjugate complex roots, if

• A. $a=1$
• B. $a^2-2a+21>0$
• C. $a^2-2a+21<0$
• D. $a^2+2a-21>0$

Answer 1

The correct option is A $a=1$

A quadratic equation $a{x}^2+bx+c=0$ will have a pair of conjugate complex roots, if all coefficients are real and $D<0$

So, for $x^2+(a-1)ix+5=0,$ coefficient of $x$ should be real,
$\Rightarrow a=1$
Also $D=0-4\times 5=-20<0$