First slide

Algebra of complex numbers

Question

$\begin{array}{l} If the equation, x^{2} + b x + 45 = 0, (b \in R) has conjugate complex roots and they satisfy \\ | z + 1 | = 2 \sqrt{10} then: \end{array}$

Moderate

A

$b^{2} + b = 12$
B

$b^{2} + b = 72$
C

$b^{2} - b = 30$
D

$b^{2} - b = 42$

Solution

$\begin{array}{l} Let z = α \pm i β be roots of the equation \\ So 2 α = - b and α^{2} + β^{2} = 45 \end{array}$
$\begin{array}{l} Now, \\ | z + 1 | = 2 \sqrt{10} \Rightarrow (α + 1)^{2} + β^{2} = 40 E l i m i n a t e β, w e g e t \\ \Rightarrow (α + 1)^{2} - α^{2} = - 5 \Rightarrow 2 α + 1 = - 5 \Rightarrow 2 α = - 6 \\ Hence b = 6 \Rightarrow b^{2} - b = 30 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App