9514 1404 393
Answer:
A) Positive (4, 2, 0), negative (0)
Explanation:
Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (with allowance for an even number of roots possibly being complex).
The signs of the coefficients are ...
- + - + -
so there are 4 sign changes. The number of positive real roots will be 4, 2, or 0.
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Changing the signs of odd-degree terms, you can use the same method to determine the number of negative real roots. With those signs changed, the signs of the coefficients are ...
- - - - -
so there are 0 sign changes. The number of negative real roots is 0.
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The graph shows there are no real roots of either sign. All the roots are complex.