Umayangana
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Can someone help solve this problem??
Roots of a Quadratic Equation
- Thread starter Umayangana
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- Nov 24, 2012
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Hello, and welcome to FMH! 
Let's look at:
[MATH]S_{n}+aS_{n-1}+bS_{n-2}=0[/MATH]
Using the definition of \(S_n\), this becomes:
[MATH](\alpha^{n}+\beta^{n})+a(\alpha^{n-1}+\beta^{n-1})+b(\alpha^{n-2}+\beta^{n-2})=0[/MATH]
What do you get upon distributing \(a\) and \(b\) and then grouping the \(\alpha\) and \(\beta\) terms together?
Let's look at:
[MATH]S_{n}+aS_{n-1}+bS_{n-2}=0[/MATH]
Using the definition of \(S_n\), this becomes:
[MATH](\alpha^{n}+\beta^{n})+a(\alpha^{n-1}+\beta^{n-1})+b(\alpha^{n-2}+\beta^{n-2})=0[/MATH]
What do you get upon distributing \(a\) and \(b\) and then grouping the \(\alpha\) and \(\beta\) terms together?