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

If the zeros of the polynomial x33x2+x+1 are ab,a,a+b, find a and b.

A
a=1 and b=±2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a=±1 and b=±2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a=2 and b=±1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a=1 and b=±2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A a=1 and b=±2
The given polynomial is x33x2+x+1
As (ab),a and (a+b) are the zeros of the given polynomial
(ab)33(ab)2+(ab)+1=0 .....(1)
a33a2+a+1=0 ....(2)
and (a+b)33(a+b)2+(a+b)+1=0 .....(3)
Putting a=1 in equation (2), we get
13+1+1=0 or 0=0
(2) is satisfied, when a=1
1 is a zero of the given polynomial
Putting a=1 in (1), we get
(1b)33(1b)2+(1b)+1=0
1b33b+3b23(12b+b2)+1b+1=0
34b+3b2b33+6b3b2=0
b3+2b=0
b(b22)=0
Either b=0 or b22=0
But b can not be zero
b2=2
b=±2
Thus, a=1 and b=±2

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving QE by Factorisation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon