SOLUTION: Use Descartes rule of signs to find the possible positive, negative, and imaginary zeroes for:
x^5 − 3x^4 + x^3 − 4x^2 + 5x − 1
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x^5 − 3x^4 + x^3 − 4x^2 + 5x − 1
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Question 1154820: Use Descartes rule of signs to find the possible positive, negative, and imaginary zeroes for:
x^5 − 3x^4 + x^3 − 4x^2 + 5x − 1 Found 2 solutions by greenestamps, MathLover1:Answer by greenestamps(13200) (Show Source):
With the polynomial in standard form (in decreasing powers of the variable), there are 5 sign changes. So the number of positive real roots is 5, or 3, or 1.
Replacing "x" with "-x" in the polynomial results in a polynomial with 0 sign changes, so there are no negative real roots.
A graph shows that in fact there are 3 positive real roots, which means there is 1 pair of imaginary roots.
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Here are the coefficients of our variable :
..... ..... ..... ..... .....
As can be seen, there are changes.
This means that there are or or real roots.
To find the number of real roots, substitute with in the given polynomial:
becomes
The coefficients are ,,,,,.
As can be seen, there are changes. This means that there are real roots.
graph shows real roots, means there will be one of roots too
