Use Descarte's rule of signs to determine the possible number of positive real zeros and negative real zeros for the function.
f(x)=2x^3-4x^2+2x+7

Question

Use Descarte's rule of signs to determine the possible number of positive real zeros and negative real zeros for the function. 
f(x)=2x^3-4x^2+2x+7

anonymous · Answer

THere should be 2 zeros

anonymous · Answer

I don't understand the rule?

anonymous · Answer

The signs change twice from positive to negative. 2x^3 -> -4x^2 ->2x
you are basically counting the number of times it goes from addition to subtraction in the problem. IE: +2x -> +7 would not count because they are both addition.

anonymous · Answer

Oh ok

anonymous · Answer

so the answer would be 2 positive real zeros. and 1 negative???

anonymous · Answer

There is only 1 real root.  A plot is attached.

anonymous · Answer

Well, it depends is the answer asking for all possible or just the definite?

anonymous · Answer

I just looked at the answer in the back. It says (2 or 0 positive; 1 negative)

anonymous · Answer

$$\{\{x\to -0.9349\},\{x\to 1.467-1.261 i\},\{x\to 1.467+1.261 i\}\} $$

anonymous · Answer

For all possible zeros, the answer I came up with is:
2 or 0 positive, 2 or 0 negative, 3 or 1 unreal

anonymous · Answer

Descarte's rule is irrelevant if one has access to the computer program, Mathematica.  One can almost plot f(x) as fast as it takes to count sign changes.

anonymous · Answer

I have a graphing program too. It shows only 1 negative real zero. But the preset rules what he is doing states that there are 3 zeros and to use descarte's rule to find them. granted saying that there is 1 negative zero on my graph would make the other 2 imaginary, but when actually using the process that the problem itself says to use, it yields different results. It's been a while since I have done descarte's rule, but it seems like the data contradicts itself. Pretty confusing. lol

anonymous · Answer

http://www.purplemath.com/modules/drofsign.htm Descartes' Rule of Signs "Descartes' Rule of Signs is a useful help for finding the zeroes of a polynomial, assuming that you don't have the graph to look at. This topic isn't so useful if you have access to a graphing calculator because, rather than having to do guess-n-check to find the zeroes (using the Rational Root Test, Descartes' Rule of Signs, synthetic division, and other tools), you can just look at the picture on the screen. But if you need to use it, the Rule is actually quite simple."