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In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

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Fibonacci Fashion

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

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Observe symmetries and engage the power of substitution to solve complicated equations.

Roots and Coefficients

Age 16 to 18 Challenge Level:

If \[z_1 z_2 z_3 = 1\] and \[z_1 + z_2 + z_3 = \frac{1}{z_1} + \frac{1}{z_2} +\frac{1}{z_3}\] then show that at least one of these numbers must be 1.

Now for the complexity! When are the other numbers real and when are they complex?