Question
The set of values of $$a \in R$$ for which $${x^2} + i\left( {a - 1} \right)x + 5 = 0$$ will have a pair of conjugate complex roots is
A.
$$R$$
B.
$$\left\{ 1 \right\}$$
C.
$$\left\{ {a\left| {{a^2} - 2a + 21 > 0} \right.} \right\}$$
D.
None of these
Answer :
$$\left\{ 1 \right\}$$
Solution :
A quadratic equation $$p{x^2} + qx + r = 0$$ can have a pair of conjugate complex roots if all coefficients are real and $$D < 0.$$
Here, $$p = 1,r = 5.\,{\text{So, }}i\left( {a - 1} \right)$$ must be real. Hence, $$a = 1$$ and then $$D < 0$$ also.