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

If (x3)(x2) is the HCF of the polynomials x22x3)(2x2+ax2) and (x2+x2)(3x2+bx3), then find the value of a & b.

Open in App
Solution

Let,
P(x)=(x22x3)(2x2+ax2) =(x+1)(x3)(2x2+ax2)

As, HCF is (x3)(x+2)
x+2=0x=2

x=2 is the zero.
P(2)=0
P(2)=(2+1)(23)2×4+a(2)2
(1)(5)(82a2)=0
5(62a)=0
a=3

Let,
Q(x)=(x2+x2)(3x2+bx3) =(x1)(x+2)(3x2+bx3)

As, HCF is (x3)(x+2)
Similarly Q(3)=0

Q(3)=(31)(3+2)(3×9+3b3)(2)(5)(27+3b3)=010(24+3b)=0b=8

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Definition of Variables
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon