Polinomlar ile ilgili çözümlü sorular
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<td>Soru1:</td>
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<td><p>`P(x)=x^{\frac{5}{n}}+(n+1).x^{n-3}+2` </p>
<p>polinomu ikinci dereceden bir polinom ise `P(-3)=?`</p></td>
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<td>Çözüm:</td>
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<td>`n-3=2,\Rightarrow n=5 `</td>
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<td>`P(x)=x^{\frac{5}{5}}+(5+1).x^{5-3}+2=6x^{2}+x+2`</td>
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<td>`P(-3)=6.(-3)^{2}+(-3)+2=6.9-3+2=54-1=53`</td>
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<td>Soru 2:</td>
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<td><p>`(a-1)x^{3}-(b+2)x^{2}-5x+7=5x^{3}+3x^{2}-cx+d-4` </p>
<p> olduğuna göre a+b+c+d toplamı kaçtır?</p></td>
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<td>Çözüm :</td>
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<td>`a-1=5 \Rightarrow a=6`,<br /></td>
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<td>`-b-2=3 \Rightarrow b=-5`,</td>
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<td>`-5=-c \Rightarrow c=5`,</td>
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<td>`7=d-4 \Rightarrow d=11`,</td>
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<td>`a+b+c+d=6-5+5+11=17`</td>
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<td>Soru 3:</td>
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<td>`\frac{7x-5}{x^{2}-2x-3}=\frac{A}{(x+1)}+\frac{B}{(x-3)}\Rightarrow A+B=?`</td>
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<td>Çözüm :</td>
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<td>`7x-5=A.(x-3)+B.(x+1)` </td>
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<td>`7x-5=Ax-3A+Bx+B`</td>
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<td>`7x-5=(A+B).x-3A+B \Rightarrow`</td>
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<td>`A+B=7 , -3A+B=-5 \Rightarrow A=3`</td>
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<td>`B=7-A \Rightarrow -3A+7-A=-5 `</td>
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<td>`B=7-3=4 , \Rightarrow A+B=3+4=7`</td>
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<td>Soru 4:</td>
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<td>`P(x)=5x^{2}-7x+3 , Q(x)=2x^{2}+3x-8 \Rightarrow<br />
`</td>
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<td>`a)P(x)+Q(x)=?, b) 2P(x)-Q(x)=?`</td>
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<td>Çözüm :</td>
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<td>`a) P(x)+Q(x)=7x^{2}-4x-5`<br /></td>
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<td>`b) 2P(x)-Q(x)=2.(5x^{2}-7x+3)-(2x^{2}+3x-8)`</td>
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<td>`2P(x)-Q(x)=10x^{2}-14x+6-2x^{2}-3x+8`</td>
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<td>`2P(x)-Q(x)=8x^{2}-17x+14`</td>
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<td>Soru 5:</td>
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<td>` der(P(x).Q(x))=8 , der(\frac{P(x)}{Q(x)})=2 \Rightarrow derP(x)=? , derQ(x)=?`</td>
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<td>` derP(x)=m , derQ(x)=n `</td>
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<td>`m+n=8 , m-n=2 \Rightarrow`</td>
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<td>`m=8-n \Rightarrow 8-n-n=2 \Rightarrow `</td>
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<td>`8-2n=2 \Rightarrow n=3 `</td>
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<td>`m=8-3=5 \Rightarrow`</td>
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<td>`derP(x)=5 , derQ(x)=3`</td>
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| Devamı .. | ||
| Polinomlar Çözümlü Sorular 1 | Polinomlar Çözümlü Sorular 2 | Polinomlar Çözümlü Sorular 3 |
| Polinomlar Çözümlü Sorular 4 | Polinomlar Çözümlü Sorular 5 | |