- #1
Theofilius
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Homework Statement
What should the coefficients a,b,c of the polinom [tex]P(x)=x^3+ax^2+bx+c[/tex] be, so his roots [tex]x_1+x_2=x_3[/tex] ?
Homework Equations
[tex]P(x)=a_n(x-c_1)(x-c_2)...(x-c_n_-_1)(x-c_n)[/tex]
[tex]c_1+c_2+...+c_n= -\frac{a_n_-_1}{a_n}[/tex]
[tex]c_1c_2+c_2c_3+...+c_n_-_1c_n= \frac{a_n_-_2}{a_n}[/tex]
[tex]c_1c_2c_3+c_1c_2c_4+...+c_n_-_2c_n_-_1c_n=-\frac{a_n_-_3}{a_n}[/tex]
.................
[tex]c_1c_2...c_n_-_1 + c_1c_2...c_n_-_2c_n+...+c_2c_3...c_n=(-1)^n^-^1 \frac{a_1}{a_n}[/tex]
[tex]c_1c_2c_3...c_n= (-1)^n \frac{a_0}{a_n}[/tex]
The Attempt at a Solution
I don't know where to start from. Anybody have any idea? Thnx for the help.
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