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Broad Topics > Advanced Algebra > Roots of equations and coefficients

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Roots and Coefficients

Stage: 5 Challenge Level: Challenge Level:1

If xyz = 1 and x+y+z =1/x + 1/y + 1/z 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?

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Fibonacci Fashion

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Janusz Asked

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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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Agile Algebra

Stage: 5 Challenge Level: Challenge Level:1

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


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