110 Views

find roots of x^3 - 2x^2 +1 if one root is 1?


Aryan Mittal 12th Jul, 2020
Answers (2)
Vaishali Sharma 12th Jul, 2020
Hello,
Divide the whole equation by (x-1)  as 1 is the root of the equation. Then you'll get a quadratic equation.
Factorise the quadratic equation, which gives you 2 remaining roots.
Rishi Garg 12th Jul, 2020

Let other roots be a and b.

Now, a+b+1 = 2 which gives  a+b = 1

and a.b.1 = -1 which gives ab = -1

putting a = 1 - b from the first equation in the second, we get

(1-b)b = -1

Solving the above equation, we get b = (1+\root(5))/2 and b = (1-\root(5))/2

hence, the other two roots are (1+\root(5))/2 and (1-\root(5))/2.

Hope this helps.

Related Questions

CLAT Current Affairs with GK ...
Apply
Stay updated with current affairs & check your preparation with the CLAT General Knowledge Mock Tests Ebook
CLAT English Language Mock Tests
Apply
Free Ebook - CLAT 2025 English Language questions with detailed solutions
ICFAI Business School-IBSAT 2024
Apply
9 IBS Campuses | Scholarships Worth Rs 10 CR
CLAT Legal Reasoning Mock Tests
Apply
Free Ebook - CLAT 2025 legal reasoning questions with detailed solutions
GIBS Business School Bangalor...
Apply
100% Placements with 220+ Companies
Great Lakes PGPM & PGDM 2025
Apply
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books