Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off


z^10-z^5-992=0 find number of roots of equation where real parts are negative


7 years ago


Answers : (2)


z10-z5-992 =(z5-32) (z5+31) = 0

The roots of z5-32 = 0 are


. You can see that here two roots will have negative real parts.


This also tells us that z5+32 = 0 will have three such roots.


So, we have a grand total of 5.



7 years ago

Dear Piyush,

first assume z^5 = t ,

then eqn becomes t2-t -992 = 0

roots are t=32,-31

1st case t = 32 ;

which means z^5 = 32 , here u can see that |z| = 2 and since this eqn is of 5th power then it will hav 5 roots with |z|= 2 and five different argument angles with 72 as a gap b/w them .i.e, 360/5=72

now draw these roots on the complex plane starting from arg=0 , then 72, 144,216,288and 360.u will get 4 imaginary roots in which 2 will lie on the left side of the plane (i.e. with negative real part , they're of arg = 144 and 216) . mod of all the 5 roots will be 2.

now in 2nd case

similar to the above one , we will hav 5 roots |z| = 1.999 , but in this case if you draw 5 roots on the imaginary plane then u will find almost similar diagram with 3 on the left side this time cauz here eqn is z^5 = -31.

thus the total no. of roots with negative real parts is 5.

7 years ago

Post Your Answer

Other Related Questions on Discuss with colleagues and IITians

kindly let me know the cutoff for assam medical entrance examination 2015.
@ aakansha there is a criteria of 50 percent of the total marks decided by the dibrugarh university. i think thats the cutoff , still prev year it was that , i mean in 2015 , but not sure...
Umakant biswal 3 months ago
Dear Akanksha why don’t you visit the official website of the institution and get to know the cutoff, merit list and also your stature there whether you ar eable to secure a seat there or...
Aneesh Sehgal 3 months ago
I have the option of joining bit mesra and daiict. Which one is better for computer science if I need to pursue MS in a foreign country and also according to the faculty
Both are should take decision based on your geographical location
Nishant Vora 3 months ago
you must go for roorkee college of engineering roorkee. This college providing you 3 years Bsc courses in Agriculture and forestery. in different fields like petroleum engineering,...
Amit Kumar Singh 3 months ago
Where can i find a reputed IIT-JEE coaching where i can get my academic doubts cleared instantly and precisely?
I can help you compare between some of the institute's which can help you decide well. 1. Bansal: Surely Bansal has a good name since it has started the trend of the classes but now the old ...
Bhushan Gupta 19 days ago
@ animesh u can always opt for askiitians , we have evrything required to crack jee . and here also u have acess to the top notch iitian and its cost effective too , here u will also get...
Umakant biswal 19 days ago
I want to get 240 in jee mains what I should do and what books I should refer can you help me get into jee mains
Physics Concepts of Physics by H.C. Verma - Volume 1 and Volume 2 Complete Physics for JEE Main 2016 by Irodov Chemistry NCERT books (only for Theory) IIT chemistry by O.P Tandon Complete...
Sourabh Singh 3 months ago
What is the minimum marks required to qualify JEE mains and advance this year for OBC?
@ rahul in jee mains the cutoff will be more than 75-80 in case of OBC , and in jee advanced it will be 9 percent in each subject and 32 percent of the total marks given by jee advanced ....
2017 years ago
today jee gave the mock allotments... according to my rank. i am getting aerospace in kharagpur.. i can also get integrated dual degree in madras and kharagpur.. probably.. which is...
Dear students, Which branch you are getting in Madras and KHaragpur. If not core then Prefer aerospace in Kgp. Thanks.
Vijay Mukati one year ago
Dear Student, If going for higher studies then only prefer integrated course. Thanks.
Vijay Mukati one year ago
correction-i am gettin aerospace itself in integrated in madras n aerspace in kharagpur.
chirag one year ago
View all Questions »

  • Complete AIPMT/AIIMS Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details

Get extra R 3,750 off

More Questions On Discuss with colleagues and IITians

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details