![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
What are the roots of $x^4+4=0$?
Given: Equation: $x^4+4=0$.
To do: To find the roots of the equation: $x^4+4=0$.
Solution:
$x^4+4=0$
$\Rightarrow x^4+4+4x^2−4x^2=0$
$\Rightarrow x^4+4x^2+4−4x^2=0$
$\Rightarrow ( x^2)^2+2.2.x^2+2^2−(2x)^2=0$
$\Rightarrow ( x^2+2)^2−(2x)^2=0$
$\Rightarrow ( x^2+2−2x)(x^2+2+2x)=0$
$\Rightarrow x^2−2x+2=0,\ x^2+2x+2=0$
$\Rightarrow x=\frac{2\pm\sqrt{4-8}}{2},\ x=\frac{-2\pm\sqrt{4-8}}{2}$
$\Rightarrow x=\frac{2\pm\sqrt{-4}}{2},\ x=\frac{-2\pm\sqrt{-4}}{2}$
$\Rightarrow x=\frac{2\pm\sqrt{4( -1)}}{2},\ x=\frac{-2\pm\sqrt{4( -1)}}{2}$
$\Rightarrow x=\frac{2\pm2\sqrt{( -1)}}{2},\ x=\frac{-2\pm2\sqrt{( -1)}}{2}$
$\Rightarrow x=\frac{2\pm2i}{2},\ x=\frac{-2\pm2i}{2}$
$\Rightarrow x=2( \frac{1\pm i}{2}),\ x=2( \frac{-1\pm i}{2})$
$\Rightarrow x=1\pm i,\ x=-1\pm i$
$\therefore x=1+i,\ 1−i,\ −1+i,\ −1−i$ are the roots of $x^4+4=0$.
Advertisements