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2014-11-08T10:20:31+05:30
It has zero +ve zeros and zero negative zeros since there is no sign change in f(x) and f(-x)

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2014-11-08T10:25:28+05:30

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Maximum number of positive zeroes of a polynomial is the number of sign changes of the coefficients in f(x).

f(x) = x^5 + 2x
number of sign changes is zero. So the maximum number of positive roots  possible is 0.

Maximum number of negative zeroes of a polynomial is the number of sign changes of the coefficients in f(-x).

f(x) = x^5 + 2x
f(-x) = (-x)^5 + 2(-x) = f(x) = -x^5 - 2x
number of sign changes is zero. So the maximum number of negative roots  possible is 0.

So there are no positive or negative roots of the polynomial.

Note: There is one root 0 which is real but it is neither positive nor negative.
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