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

If p(x) is a polynomial of degree greater than 2 such that p(x) leaves remainder a and −a when divided by x+a and x−a respectively. If p(x) is divided by x2−a2 then remainder is

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

The correct option is D −xAs degree of remainder is always lesser than degree of divisor,we have taken remainder with degree less than 2 here. Let ux+v be the remainder when p(x) is divided by (x2−a2) Using division algorithm, p(x)=(x2−a2)q(x)+(ux+v)⋯(i) where q(x) is the quotient. We know that, by remainder theorem, p(−a)=a, p(a)=−a Putting x=a and x=−a in the equation (i), a=−ua+v−a=ua+v Solving them simultaneously, ⇒v=0⇒u=−1 Hence, the required remainder is ux+v=−x+0=−x

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
General Solution of tanθ = tanα
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program