According to Descartes' rule of signs, how many possible negative real roots could the following polynomial function have?

Question

According to Descartes' rule of signs, how many possible negative real roots could the following polynomial function have?
                               F(x)=3x^4-5x^3+5x^2+5x-2
Four
Three
One
Two or zero

 

 

Identify the relative minimum value for the function shown below.
                  G(x)=x^3-3x^2+2

Answer 1

Descartes' rule of signs:  http://www.purplemath.com/modules/drofsign.htm

 

For POSITIVE zeroes, check the polynomial "as is".  And as you've written it, the sign changes 3 times.  This means you could have three positive zeroes OR just 1.  (They'll drop off in groups of 2, if they are imaginary)

 

For NEGATIVE zeroes, we have to rewrite the polynomial as f(-x), or 3x⁴+5x³+5x²-5x-2

 

This polynomial changes signs just once, so you will have the 1 negative zero.