5 of 5 Items .... Type: Impossible Problem

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Let \( f(x) = 2x^3 + bx^2 + cx + d\). Find integers b, c and d such that \(f(\frac{1}{4}) = 0\).

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Try to find six consecutive integers that sum to 342

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Find the cubic polynomial with integer coefficients that has three complex roots.

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I invite students to create an unfair coin — one that is biased toward coming up heads or tails — that has the following property: When the coin is flipped twice, the results of the two flips are more likely to be different than the same. In other words, you’re more likely to get heads and tails than to get heads and heads or tails and tails.

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Construct a convex octagon with four right angles.

Does this one work?