SOLUTION: Possible number of imaginary zeros in g(X)=x^4+3x^3+7x^2-6x-13

Question 1010745: Possible number of imaginary zeros in g(X)=x^4+3x^3+7x^2-6x-13
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The analysis you are using is called Descartes' rule of signs.
When you have determined the number of sign changes for , then you know the (maximum) possible number of positive zeros for your function.
You then have to evaluate to get the (maximum) possible number of zeros.
Positive and negative possible zeros always decrease by two's. You can't go below none.
In your problem:

there are sign changes for , which means there is positive real zero
now, rewrite the given polynomial by substituting for :

there are sign changes for , which means there are a of negative real zeros
since we have degree function,means there are zeros in all, and we know that complex zeros come in pairs, it means there will be negative zero and imaginary or complex zeros
so, in all will be:
positive real zero
negative real zero
complex zeros

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