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Part of 2009 BMO TST

Problems(1)

Albanian BMO TST 2009 Question 1

Source:

6/4/2010
Given the equation x4−x3−1=0x^4-x^3-1=0 (a) Find the number of its real roots. (b) We denote by SS the sum of the real roots and by PP their product. Prove that P<−1110P< - \frac{11}{10} and S>611S> \frac {6}{11}.
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