SOLUTION: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4.      Log On


   

Question 43582: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29+=+9x%5E3+-+7x%5E2+%2B+10x+-+4
Look at the value coefficients: +9 then -7 then +10 then -4
The sign changes three times, so you have a chance of three positive real roots.
g%28-x%29+=+9%28-x%29%5E3+-+7%28-x%29%5E2+%2B+10%28-x%29+-+4
g%28-x%29+=+-9x+-+7x+-+10x+-+4
Look at the value coefficients: -9 then -7 then -10 then -4
The sign never changes, so you obviously know that there are absolutely no negative real roots.
Pos: .. 3 .. 1
Neg: . 0 .. 0
Imag: 0 .. 2
You can take two away from the positives and add to the imaginery.