1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Find all the zeros of 2x4−9x3+5x2+3x−1, if two of its zeros are 2+√3 and 2−√3

A
2, 3, 1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4, 7, -1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
6, 5, 8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D None of theseLet, p(x)=2x4−9x3+5x2+3x−1 Since, 2+√3 and 2−√3 are zeros of p(x)⇒(x−2−√3) and (x−2+√3) divides p(x) (∵Factor thm.)⇒(x−2−√3)(x−2+√3) divides p(x)⇒(x2−4x+1) divides p(x)x2−4x+1)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2x4−9x3+5x2+3x−1( 2x2−x−1 2−x4−+8x3+−2x2–––––––––––––––– −x3+3x2+3x−1 −+x3+−4x2−+x––––––––––––––– −x2+4x−1 −+x2+−4x−+1–––––––––––––– 0Now, the other zeros can be obtained from on solving 2x2−x−1=0⇒2x2−2x+x−1=0⇒2x(x−1)+1(x−1)=0⇒(2x+1)(x−1)=0⇒x=−12,1Hence, all the zeros are −12,1,2+√3,2−√3

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Division of Algebraic Expressions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program