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September 18th, 2011, 07:38 AM   #1
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Precalculus

When we using Descarte's Rules of Sign

if the functions like: f(x) = 4x^3 - 5x + 8
how do we know how many variation sign that it has??
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September 18th, 2011, 08:55 AM   #2
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The coefficients are positive, negative and positive (in that order), so there are two changes of sign. Hence f(x) has either two positive zeros or no positive zeros. In fact, it has no positive zeros.

The coefficients of f(-x) are -4, 5, 8, so f(-x) has one change of sign, and that tells you that f(x) has exactly one negative zero.
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