wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

p(x)=x3+8x27x+12 and g(x)=x1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If a is the degree of q(x) and b is the degree of r(x), (ab)=?.


A

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 2
Remainder =r(x)=p(1)=13+8×127×1+12=14
The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials.
So, Degree of r(x)=b=0
q(x)=p(x)g(x)
Now , p(x)=x3+8x27x+12
g(x)=(x1)
Performing long division

x2+9x+2x1)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x3+8x27x+12 x3x2 () (+) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 9x27x 9x29x () (+) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ +2x+12 2x2 () (+) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 14

q(x)=p(x)g(x)=x2+9x+2
So, degree of q(x)=a=2
Hence, ab=20=2

flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q4
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon