Question

If the equation, $x^2 + bx + 45 = 0$ $\left(b\epsilon R\right)$ has conjugate complex roots and they satisfy $\left|z+1\right| = 2\sqrt{10},$ then :

• A. $b^2 + b = 12$
• B. $b^2 - b = 42$
• C. $b^2 - b = 30$
• D. $b^2 + b = 72$

Answer 1

Answer: (C)

Assuming $z$ is a root of the given equation,
$z=\frac{-b\pm i\sqrt{180-b^{2}}}{2}$
so, $\left(1-\frac{b}{2}\right)^{2}+\frac{180-b^{2}}{4}=40$
$\Rightarrow -4b+184=160 \Rightarrow b=6$