f(x) =5x^4 -10X^3+X^2-2.5X+20

Question

find the maximum number of zeros and Descarte's rule of signs to determine how many positive and negative zeros the function has.  Show work

Answer 1

f(x) = 5x^4 - 10x^3 + x^2 - 2.5x + 20

because it is to the 4th power there are up to 4 roots.

by Descarte's there are 4 changes from positive to negative.  So there up to 4 real roots and 2 maybe real and 2 complex.

So, there may be 0 to 4 real roots.

2 maybe complex.

f(-x) = 5(-x)^4 - 10(-x)^3 + (-x)^2 - 2.5(-x) + 20

f(-x) = 5x^4 + 10x^3 + x^2 + 2.5x + 20

there are no negative roots

 

Comments

You have been the knight in shining armor  -  thank you