Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If least and largest real value of   , for which the equation  <img alt="z+\alpha\left | z-1 \right |+2i=0\left ( z\in C \text{ and } i=\sqrt{-1} \right )"

If least and largest real value of  \alpha , for which the equation  z+\alpha\left | z-1 \right |+2i=0\left ( z\in C \text{ and } i=\sqrt{-1} \right ) has a solution, are p and  q respectively ; then 4\left ( p^2 +q^2\right )is equal to_____
Option: 1 5
Option: 2 10
Option: 3 20
Option: 4 25

Answers (1)

best_answer

 

\mathrm{z}+\alpha|z-1|+2 \mathrm{i}=0

\\\mathrm{x}+\mathrm{i} \mathrm{y}+\alpha \sqrt{(\mathrm{x}-1)^{2}+\mathrm{y}^{2}}+2 \mathrm{i}=0 \\ \\\therefore \quad \mathrm{y}+2=0 \text { and } \mathrm{x}+\alpha \sqrt{(\mathrm{x}-1)^{2}+\mathrm{y}^{2}}=0 \\ \\\mathrm{y}=-2 \qquad\& \qquad\mathrm{x}^{2}=\alpha^{2}\left(\mathrm{x}^{2}-2 \mathrm{x}+1+4\right)

\\\alpha^{2}=\frac{x^{2}}{x^{2}-2 x+5} \\ \\\alpha^{2} \in\left[0, \frac{5}{4}\right] \\ \\\therefore \quad \alpha^{2} \in\left[0, \frac{5}{4}\right] \\ \\\therefore \quad \alpha \in\left[-\frac{\sqrt{5}}{2}, \frac{\sqrt{5}}{2}\right]

\text { then } 4\left[\left(p\right)^{2}+\left(q\right)^{2}\right]=4\left[\frac{5}{4}+\frac{5}{4}\right]=10

Posted by

Suraj Bhandari

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question