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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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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

Stage: 5 Challenge Level: Challenge Level:1

The hint is in the title here!


If $z_1z_2z_3=1$ what can you say about ${1\over z_1} + {1\over z_2} + {1\over z_3}$?