Question

9. In one state, the number of bicycles sold in the year 2002-2003 was

7,43,000. In the year 2003-2004, the number of bicycles sold was 8,00,100. In

which year were more bicycles sold? and how many more?​

Answer 1

Answer:

P(x) = x ^ 5 + 2x ^ 3 + x ^ 2 + 2 g(x) = x + 2

Put 2x+3=0, we get x=−23. < /p > < p > < /p > < p > < /p > < p > Substitute x=−23 in f(x)=2x3+6x2+4x as follows: < /p > < p > < /p > < p > < /p > < p > f(x)=2x3+6x2+4x < /p > < p > < /p > < p > < /p > < p > f(−23)=2(−23)3+6(−23)2+4(−23) < /p > < p > < /p > < p > < /p > < p > f(−23)=2(−827)+6(49)−6 < /p > < p > < /p > < p > < /p > < p > f(−23)=−427+454−6 < /p > < p > < /p > < p > < /p > < p > f(−23)=427−6 < /p > < p > < /p > < p > < /p > < p > f(−23)=43 < /p > < p > < /p > < p > < /p > < p > Now substitute x=−23 in g(x)=x2+3x+2 as follows: < /p > < p > < /p > < p > < /p > < p > g(x)=x2+3x+2 < /p > < p > < /p > < p > < /p > < p > g(−23)=(−23)2+3(−23)+2 < /p > < p > < /p > < p > < /p > < p > g(−23)=49−29+2 < /p > < p > < /p > < p > < /p > < p > g(−23)=49−18+8g(−23)=−41 < /p > < p > < /p > < p > < /p > < p > Finally substituting x=−23 in the polynomial p(x)=f(x)+3g(x) we get, < /p > < p > < /p > < p > < /p > < p > p(x)=f(x)+3g(x) < /p > < p > < /p > < p > < /p > < p > p(−23)=f(−23)+3g(−23) < /p > < p > < /p > < p > < /p > < p > p(−23)=43+3(−41) < /p > < p > < /p > < p > < /p > < p > p(−23)=43−43 < /p > < p > < /p > < p > < /p > < p > p(−23)=0 < /p > < p > < /p > < p > < /p > < p > Hence, the polynomial p(x)=f(x)+3g(x) is divisible by 2x+3. < /p > < p > < /p > < p >Put 2x+3=0,weget x=−23.</p><p></p><p></p><p>Substitute x=−23 in f(x)=2x3+6x2+4x asfollows:</p><p></p><p></p><p>f(x)=2x3+6x2+4x</p><p></p><p></p><p>f(−23)=2(−23)3+6(−23)2+4(−23)</p><p></p><p></p><p>f(−23)=2(−827)+6(49)−6 </p><p></p><p></p><p>f(−23)=−427+454−6 </p><p></p><p></p><p>f(−23)=427−6 </p><p></p><p></p><p>f(−23)=43 </p><p></p><p></p><p>Nowsubstitute x=−23 in g(x)=x2+3x+2 asfollows:</p><p></p><p></p><p>g(x)=x2+3x+2 </p><p></p><p></p><p>g(−23)=(−23)2+3(−23)+2 </p><p></p><p></p><p>g(−23)=49−29+2 </p><p></p><p></p><p>g(−23)=49−18+8g(−23)=−41</p><p></p><p></p><p>Finallysubstituting x=−23 inthepolynomial p(x)=f(x)+3g(x) weget,</p><p></p><p></p><p>p(x)=f(x)+3g(x) </p><p></p><p></p><p>p(−23)=f(−23)+3g(−23)</p><p></p><p></p><p>p(−23)=43+3(−41)</p><p></p><p></p><p>p(−23)=43−43 </p><p></p><p></p><p>p(−23)=0</p><p></p><p></p><p>Hence,thepolynomial p(x)=f(x)+3g(x) isdivisibleby 2x+3.</p><p></p><p>