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The polynomials P(t) = 4t3 - st2 + 7 and Q(t) = t2 + st + 8 leave the same remainder when divided by (t - 1). Find the value of s.

Posted by Aditi Singh 2 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Shanu Pratap 2 years, 3 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+7p(t)=4t3−st2+7 q(t)=t2+st+8q(t)=t2+st+8 Using remainder theorem the remainder of p(t)t−1p(t)t−1is p(1) and the remainder ofq(t)t−1q(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−sp(1)=4(1)3−s(1)2+7⇒4−s+7=11−s q(1)=(1)2+s(1)+8=1+s+8=9+sq(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

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CBSE > Class 09 > Mathematics