SOLUTION: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4. I must show my work. This is from a worksheet and I'm not sure how to

Algebra ->  College  -> Linear Algebra -> SOLUTION: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4. I must show my work. This is from a worksheet and I'm not sure how to       Log On


   

Question 166495: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4.
I must show my work. This is from a worksheet and I'm not sure how to do it.
Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
State the number of positive real zeros, negative real zeros, and imaginary zeros for
g(x)=9x^3-7x^2+10x-4.
g(-x) = -9x^2 - 7x^2 - 10x -4
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Using DesCartes Rule of Signs:
# of changes of sign in g(x) = 3; so 1 or 3 positive Real roots
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# of changes of sign in g(-x) = 0; so 0 negative Real Roots
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# of imaginary zeroes is 0 or two because g(x) is a cubic
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Comment: graphing g(x) is find it has one positive Real Root.
So it must have 2 imaginary roots.
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Cheers,
Stan H.