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Polynomials (id: f204081ab)

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admin 发表于 2024-6-15 15:22:37 | 显示全部楼层 |阅读模式
本题目来源于试卷: Polynomials,类别为 IB数学

[填空题]
Consider the polynomkcmd9 1.rjf 9vn(k)w jial r(6(r0 ke)lxbjfc9fz $p(z)=z^{5}+z^{4}-z^{3}+z^{2}+4 z+2$ , for $z \in \mathbb{C}$ .
1. Write down the sum and product of the roots of p(z)=0 .sum of roots =    product of roots =   
2. Show that (z+1) is a factor of p(z) .

The polynomial can be written in the form $p(z)=(z+1)^{3}\left(z^{2}+c z+d\right)$ .
3. Find the value of c and the value of d .d =    c =   
4. Hence find the complex roots of p(z)=0 .    $\pm \mathrm{i}$




参考答案:
空格1: -1空格2: -2空格3: 2空格4: -2空格5: 1


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