|Apr18-12, 12:09 AM||#1|
Cubic polynomial function with 3 real roots; one at infinity?
Is it possible to have a cubic polynomial (ax^3+bx^2+cx+d) which has three REAL roots, with one of them being +/- infinity?
If there is, can you give an example?
|Apr18-12, 12:44 AM||#2|
But we could still ask if there's a 3rd degree polynomial such that the limit as x->inf is 0. The answer's no, and it's easy to see. As x -> +inf, x^3 goes to +inf. Since the x^3 term eventually dominates the rest of the terms, the polynomial goes to +inf.
Likewise, as x -> -inf, the function must go to -inf. So it's not possible for the polynomial to go to zero at +/- infinity. This reasoning goes through for any odd-degree polynomial. For even-degree polynomials, the limits at +/- infinity are both infinity.
|Apr18-12, 01:29 AM||#3|
Many thanks for the enlightenment, Steve! Cheers.
|cubic, infinity, polynomial, roots|
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