Relationships Between the Roots of Quadratic Equations
Given a quadratic equation `ax^2+bx+c=0` whose solutions are `x_{1,2}={-b+-sqrt{b^2-4ac}}/{2a}`.
A: Show that Vieta's formulas hold: `x_1x_2=c/a` `x_1+x_2=-b/a,`.
B: Express the following in terms of a, b, c: `1/{x_1^2}+1/{x_2^2}` `1/x_1+1/x_2, ` `x_1^3+x_2^3,` `x_1^2+x_2^2`.
Difficulty level (1 very easy - 10 very hard): 4
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