Let P be a polynomial with integer (real) coefficients such that; (1) - the coefficient of the leading term and the independent term (counted as the coefficient of x^0 - 0 degree) are odd; (2) - The total number of odd coefficients (odd here refers to the coefficient itself, not to the degree of its corresponding term) is odd.
Like in
P(x) = x^3 - 5x^2 + 2x -7
P(x) = 9x^3 - 6 x^2 + 3x -5
P(x) = x^4 +5x^3 + 7x^2 + x +1
P(x) = 7x^5 + 2x^4 - x^3 + + 2x^2 - 8x -3
Show that P has no root such that both the real and the imaginary parts are rational. In other words, if a + bi is a root of P, then at least one of the numbers a and b is irrational.
2007-11-23
04:49:02
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5 answers
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asked by
Steiner
7