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Problem

In the quadratic ${\underline \qquad} x^2 + {\underline \qquad} x + {\underline \qquad}$, first Al says "real" or "complex" for the roots of the quadratic. Then Betty fills in one of the blanks with a real number, and then Al fills one in, and finally Betty fills one in. If the roots are as Al declared, then he wins, otherwise Betty wins.

a) Which player should win if Al says "real"? What is the winning strategy?
b) Which player should win if Al says "complex"? What is the winning strategy?
c) Who wins the game if Al says "real" when the polynomial is $x^4 + {\underline \qquad} x^3 + {\underline \qquad} x^2 + {\underline \qquad} x + 1$ instead? (How will you judge it if some roots are real and some are complex?)
d) What happens when Al says "complex" with this polynomial?

Details
Contributer: Josh
Authors
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References
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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