If the equation, x2 + bx + 45 = 0 (bϵ R) has conjugate complex roots and they satisfy |z+1| = 2√10, then :

Question

If the equation, x2 + bx + 45 = 0 (bϵ R) has conjugate complex roots and they satisfy |z+1| = 2√10, then : (A) b2 + b = 12 (B) b2 - b = 42 (C) b2 - b = 30 (D) b2 + b = 72

Tardigrade Admin · Accepted Answer

Assuming z is a root of the given equation, z=(-b± i√180-b2/2) so, (1-(b/2))2+(180-b2/4)=40 ⇒ -4b+184=160 ⇒ b=6

Q. If the equation, $x^{2} + b x + 45 = 0$ $(b ϵ R)$ has conjugate complex roots and they satisfy $∣ z + 1 ∣ = 210,$ then :

$b^{2} + b = 12$

$b^{2} - b = 42$

$b^{2} - b = 30$

$b^{2} + b = 72$

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

Q. If the equation, x2+bx+45=0 (bϵR) has conjugate complex roots and they satisfy ∣z+1∣=210​, then :

b2+b=12

b2−b=42

b2−b=30

b2+b=72