The polynomials p(t)=4t³-st²+7andq(t)=t²+st+8 leave the same …
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Yogita Ingle 4 years, 10 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
{tex}p(t)=4t^3-st^2+7{/tex}
{tex}q(t)=t^2+st+8{/tex}
Using remainder theorem the remainder of {tex}\frac{p(t)}{t-1} {/tex}is p(1) and the remainder of{tex} \frac{q(t)}{t-1}{/tex} is q(1).
Substitute t=1 in the given functions.
{tex}p(1)=4(1)^3-s(1)^2+7\Rightarrow 4-s+7=11-s{/tex}
{tex}q(1)=(1)^2+s(1)+8=1+s+8=9+s{/tex}
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
Therefore, the value of s is 1.
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