Question

The polynomials P(t) = 4t^3 - st^2 + 7 and Q(t) = t^2 + st + 8 leave the same remainder when divided by (t-1). Find the value of s.​

Answer 1

Step-by-step explanation:

Yogita Ingle 1 year, 8 months ago

Remainder theorem: If a polynomial P(x) is divided by (x-c), then the remainder is equal to P(c).

The given polynomial are

p(t)=4t3−st2+7

q(t)=t2+st+8

Using remainder theorem the remainder of p(t)t−1is p(1) and the remainder ofq(t)t−1 is q(1).

Substitute t=1 in the given functions.

p(1)=4(1)3−s(1)2+7⇒4−s+7=11−s

q(1)=(1)2+s(1)+8=1+s+8=9+s

It is given that if p(t) and q(t) divided by (t-1), then the remainder is same.

p(1)=q(1)

Substitute these values.

11-s=9+s

Add s on both sides.

11=9+s+s

11=9+2s

Subtract 9 from both sides.

11-9=2s

2=2s

Divide both sides by 2.

1=s